Fractional quantum Hall states are a cornerstone of topological physics, hosting fractionally charged quasiparticles with exotic statistics that promise to enable topologically protected quantum information processing. Among these, the Pfaffian state introduced by Moore and Read implements a p-wave pairing structure that supports excitations with non-Abelian exchange statistics. Despite extensive study in electronic systems, direct access to its pairing structure has remained limited. Here we realize a three-particle bosonic Pfaffian state of ultracold $^{87}\mathrm{Rb}$ atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field. Using a Bayesian-optimized adiabatic protocol, we prepare a state exhibiting Pfaffian pairing correlations. Site-resolved measurements of multi-point density correlations reveal a pronounced suppression of short-range three-body coincidences, reflecting the underlying pairing structure. We further probe the state's transport response through Hall drift measurements. Our results establish a bottom-up approach to engineering non-Abelian topological order and lay the groundwork for future explorations of anyonic braiding in synthetic matter.

The interplay among superconductivity, magnetism, and nontrivial band topology represents one of the most compelling frontiers in condensed matter physics. The exploration of novel superconductivity in 3d transition-metal compounds, particularly the rare Cr-based systems containing strongly magnetic Cr ions, has long attracted attention owing to their unconventional pairing mechanisms that challenge conventional wisdom. Yet, Cr-based superconductors remain scarce, especially those possessing nontrivial topological character, underscoring the urgent need to uncover new members. Here we report the observation of superconductivity in pressure-amorphized Cr-based topological insulator CrP$_4$. Upon compression, CrP$_4$ undergoes an anomalous quantum phase transition from a metallic to a semiconducting-like state at around 15 GPa, driven by significant changes in the electronic structure. At approximately 70 GPa, re-metallization with superconductivity occurs alongside an irreversible amorphization. The superconducting transition temperature Tc increases monotonically with pressure, reaching 4.8 K at 141.3 GPa. Furthermore, theoretical calculations predict multiple topological phase transitions from a strong topological insulator to a trivial state and finally back to a strong topological state under pressure. Our study not only establishes CrP$_4$ as the first Cr-based amorphous superconductor but also opens a new paradigm for exploring superconducting and topological properties in amorphous materials.

CeSiI is a van der Waals heavy-fermion metal recently found to exhibit unconventional superconductivity near a pressure-induced antiferromagnetic quantum critical point (QCP) at Pc =6 GPa. Here, we report a comprehensive single-crystal X-ray diffraction study of CeSiI under high pressures up to 8.3 GPa at room temperature, revealing subtle structural responses that precede pressure-driven QCP. We find that the unit-cell volume decreases smoothly upon compression without showing any structural phase transition in the investigated pressure range. Intriguingly, we observe abrupt and concurrent anisotropic responses of the lattice parameters around Pc =6 GPa, i.e., the a-axis contracts while the c-axis enlongated suddenly, with the unit-cell volume smoothily varies with pressure. Structural refinements further show that these lattice anomalies primarily originate from changes of Ce-Ce and Ce-Si bond lengths, as well as a flattening of the inner honeycomb Si layer within the CeSiI monolayer around Pc. Our findings establish an interesting case linking pressure-driven electronic transition of QCP at low temperatures to incipient structural responses at room temperature, thereby providing fresh insight into the pressure-temperature phase diagram of CeSiI.

To gain deeper insight into the role of hole kinetics in determining magnetism in highly frustrated doped Mott insulators, we consider the single-hole counter-Nagaoka problem on the kagome lattice, using magnetization as a tuning parameter. Near full polarization, a doped hole delocalizes upon binding reversed spins in a pattern of singlet bonds which we term resonating-valence-bond (RVB) polaron. These RVB polarons can have extremely small effective bandwidths, and hence exhibit self-trapping. By tuning the spin polarization, we track the evolution of these states toward the unpolarized sector, where we observe the emergence of $\sqrt{3}\times\sqrt{3}$ antiferromagnetic correlation reminiscent of the classical Potts and Heisenberg models on the kagome lattice. These results provide a framework to understand how RVB physics at short scales evolves into conventional magnetic correlations at long scales.

Single-wall carbon nanotubes (SWCNTs) are narrow ribbons of graphene with atomically precise edges and a single quantum transport channel, at experimentally-relevant dopings. This makes them ideal systems to harness quantum transport straintronics (QTS), i.e. using mechanical strain to control accurately quantum transport. We present QTS data from three single-wall carbon nanotube quantum dot (SWCNT-QD) transistors over a broad range of in-situ tunable and reversible uniaxial strain ($\Delta\varepsilon_\text{mech}\approx$ 0 to 3 %). We first present the nanofabrication of the suspended SWCNT transistors whose channel lengths are $\approx$ 30 nm. The channels are strained by moving gold clamps holding firmly the nanotubes. We present detailed charge transport data, $dI/dV_{\text{B}} - V_{\text{B}} - V_{\text{G}}$ and $dI/dV_{\text{B}} - V_{\text{B}} - \Delta\varepsilon_\text{mech}$, showing a large mechanical-gating effect of the SWCNT-QDs. The precise reversibility of the data, and their agreement with QTS theory, confirms that the tubes are strained elastically. We demonstrate that the mechanical control of the QD doping is not due to capacitive-gating effects, but to quantitatively predictable bandstructure changes including a strain-tunable bandgap. This precise mechanical control of the doping and bandgap of SWCNT-QDs could find applications in qubits, condensed matter physics, and homojunction molecular transistors.

How do we detect topological phases from a single ground state? Entanglement entropy and spectrum have long been the standard tools -- but the reduced density matrix (RDM) itself contains far more information. We show that the RDM of a 2D topologically ordered system, expressed at the entanglement cut, realizes a 1D mixed-state phase. For the $\mathbb{Z}_2$ toric code phase, it is a 1D $\mathbb{Z}_2$ strong-to-weak spontaneous symmetry breaking (SW-SSB) phase, where deconfinement of anyons manifests as the short-range correlation of both $\mathbb{Z}_2$ charge and $\mathbb{Z}_2$ domain-wall in the RDM. The bulk $e$-$m$ duality translates into a Kramers--Wannier self-duality of the SW-SSB phase. Extending the framework to gapped $\mathbb{Z}_2$ spin liquids, the global spin-rotation symmetry manifests as an additional weak symmetry for the 1D RDM. Spin-$\frac{1}{2}$ spinons result in a cusp on the disorder parameter of spin-rotation at $\theta=\pi$, providing a direct, ground-state signature of symmetry fractionalization. We verify this prediction analytically using the matrix product density operator formalism and numerically for the kagome-lattice resonating valence bond state. The proposed observable requires only a single ground-state wavefunction, making it amenable to quantum simulation platforms.

Kagome FeGe hosts a $2\times2\times2$ charge-density wave (CDW) that strongly interplays with antiferromagnetic order. Here, we report $^{57}$Fe nuclear resonant scattering measurement to study FeGe across its long-range CDW and incommensurate magnetic transitions. Upon entering the CDW state, hardening of acoustic phonons and optical phonons around 22~meV, 27~meV, and 31~meV are observed in the Fe partial phonon density of states, which can be qualitatively captured by first-principle calculations. Upon entering the incommensurate magnetic phase, neither the phonon density of states nor the hyperfine interaction parameters change significantly, although a subtle feature associated with the incommensurate magnetic order or slow fluctuations is detected in the time-domain Mössbauer spectra. These findings show that the CDW in kagome FeGe significantly modifies its lattice dynamics and magnetism, evidencing an intertwined nature of the spin, charge, and lattice degrees of freedom.

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh$_6$Ge$_4$ has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4\textit{f} electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4\textit{f} shell in CeRh$_6$Ge$_4$ using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4\textit{f} with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field (CEF) sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the non crossing approximation (SIAM/NCA). The Kondo effect mixes higher lying crystal-field states into a resulting multiorbital ground state with 4\textit{f} occupancy \textit{n}$_f$\,$\sim$\,0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh$_6$Ge$_4$.

Trace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators. Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization. The key idea is to combine Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero. Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.

Altermagnetism establishes momentum-dependent spin splitting through non-symmorphic crystal symmetries, yet whether these same symmetries simultaneously govern spin and lattice collective excitations remains open. Here we show, using first-principles calculations and linear spin-wave theory, that monolayer CuF$_2$ hosts both chirality-split magnons and cycloidal phonons controlled by the same $P2_1/c$ symmetry operations. The altermagnetic order drives strongly anisotropic magnon chirality via symmetric anisotropic exchange, with Dzyaloshinskii--Moriya interactions acting as a weak secondary modulation. Crucially, the phonon and magnon chiral responses are directionally complementary: cycloidal phonon angular momentum emerges precisely where magnon chirality is symmetry-suppressed, and vice versa. The magnon bands further carry quantized Chern numbers $C^M = \pm 2$, confirming non-trivial altermagnetic topology. These results establish monolayer CuF$_2$ as a platform where a single symmetry framework engineers magnonic, phononic, and topological responses, providing a direct connection between altermagnetism and spin-lattice chirality in two-dimensional materials.

By forming hybrid light-matter states, optical cavities offer a route for engineering material properties, however, unambiguously probing the effects of light-matter coupling remains difficult. Here, we show that the polarization-resolved statistics of photons transmitted through a cavity, measurable via $g^{(2)}$, provide one such diagnostic. By relating $g^{(2)}$ to matter correlation functions such as the Raman structure factor, we link photon bunching and antibunching to material properties. By applying this method to the stripy-to-antiferromagnetic transition in the Kitaev-Heisenberg spin model, we find that polarization-dependent patterns of bunching and antibunching encode the magnetic point-group symmetries of each phase and characterize the behavior at the phase boundary. Finally, we predict measuring $g^{(2)}$ for output photon pairs polarized orthogonal to the input field will isolate higher-order light-matter scattering processes that probe higher-order material correlations.

Non-invertible symmetries in quantum many-body systems generally give rise to sequential unitary circuits that move symmetry defects. In this paper, we investigate invariants defined by sequences of such circuits, which move non-invertible defects and generate a Berry phase evaluated on quantum states with defects. We show that this Berry phase generally defines an invariant under local deformations, provided that the sequential circuits preserve the locality of those deformations. This invariant also rules out a short-range-entangled state that preserves the non-invertible symmetry, thereby signaling the 't Hooft anomaly of a non-invertible symmetry purely in terms of unitary operators acting on a state. We then apply this framework to loop excitations in three spatial dimensions and identify a new loop excitation in the (3+1)D $\mathbb{D}_4$ topological order, which we dub a non-Abelian fermionic loop. Using the invariant of sequential circuits, we characterize the statistics of non-Abelian fermionic loops. In addition, we find a new (3+1)D mixed topological order with a single non-Abelian fermionic loop, whose long-range entanglement is protected by an invariant of sequential circuits.

Unraveling the mechanism that binds electrons into Cooper pairs in cuprate high-temperature superconductors remains one of the most fundamental challenges in condensed-matter physics. While both magnetic interactions and lattice vibrations are known to govern key electronic properties, their possible cooperation has never been directly observed. We investigate HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ (Hg1223) - the cuprate with the highest $T_{\mathrm{c}}$ at ambient pressure - as a magnifying glass to probe the possible entwining of the excitations at the core of the pairing. Using resonant inelastic X-ray scattering, we find that the charge response is dominated by dynamic charge density fluctuations (CDF) extending up to several hundred meV, where magnetic excitations reside. At the same momentum where CDF are most intense, the paramagnon energy exhibits a pronounced softening, revealing a strong interplay among charge, lattice, and spin excitations. Our results point to a cooperative mechanism in which dynamic charge fluctuations mediate the coupling between lattice, charge and spin degrees of freedom-shedding new light on the fundamental origin of high-$T_{\mathrm{c}}$ superconductivity.

Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during storage and transmission. The handbook includes descriptions of these error-correcting codes and a classification according to the symbols they use. It also catalogues relations among codes and related objects such as sphere packings, lattices, designs, groups, and classical and quantum phases of matter. The collection is intended both as a rigorous reference and as a practical aid for tracing the web of code relationships and uncovering new connections.

Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems, a prime example being spectral singularities known as exceptional points. Their relevance in, e.g., quantum sensing, unidirectional transport, and robust lasing makes it important to be able to identify exceptional points through observable features of a many-body system. Here, using as an example a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, we develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian, which in a non-Hermitian system are no longer the adjoint of each other. We first show that a global measure constructed from the difference between the Hamiltonian and its adjoint locates exceptional points via distinct non-analytic behavior. At the level of observables, differences in local spin correlations evaluated on the right and left eigenstates provide a reliable static detection scheme. In contrast, static bipartite entanglement measures fail to capture this distinction, urging us to study the quantum dynamics of the model. Following a sudden quench, we demonstrate that the time-averaged right-left entanglement entropy difference directly encodes signatures of the exceptional point. In the RT-symmetric regime, it exhibits a pronounced peak at the exceptional point, whereas in the PT-symmetric regime it behaves as an order-parameter-like quantity, remaining finite in one phase and vanishing at the transition. Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points, providing a practical route to identify them in existing quantum simulators.

We investigate the nonequilibrium dynamics of a one-dimensional interacting system across a transition from a charge-density-wave (CDW) phase to a symmetry-protected topological (SPT) phase. Starting from a CDW initial state, we study both sudden quenches and slow ramps into the SPT regime. While the CDW order melts under both protocols, the fate of topological order is sharply different. Following a sudden quench, long-range SPT order does not emerge because the post-quench state contains a finite density of excitations above the topological ground state. In contrast, slow ramps allow the system to follow the instantaneous ground state away from the critical region, enabling the buildup of SPT order with deviations governed by Kibble-Zurek defect production. The dynamics is solvable via a unitary mapping to a quadratic fermionic Hamiltonian, allowing us to compute the Loschmidt echo, correlation functions, and string correlator. The Loschmidt rate function exhibits cusps signaling dynamical quantum phase transitions, while the correlation dynamics reveal the contrasting mechanisms governing quenches and ramps across the transition. These results demonstrate that entering the topological regime is not sufficient for the emergence of topological order; the decisive factor is the suppression of excitation production during the evolution.

We present a mechanism for ferromagnetism in narrow bands consisting of Anderson-localized states. We exploit single-particle localization to derive a controlled theory of exchange interactions within the narrow band. For quasiperiodic systems with a half-filled moiré band, we show that the critical interaction strength for ferromagnetism is highly sensitive to the geometry of real-space overlaps between localized orbitals: we find well-defined resonances at which ferromagnetism sets in for interaction energies that are far lower than the gap to other bands. Near these resonances, all the approximations in our theory are controlled, so our critical point predictions are quantitative. We show examples both in one and two dimensions. Our work identifies a route to ferromagnetism based on the geometry of real-space wavefunctions, distinct from previously found mechanisms based on the quantum geometry of Bloch bands.

Accurate modeling of quantum many-body systems often requires computationally expensive simulations such as Density Matrix Renormalization Group (DMRG) or Quantum Monte Carlo (QMC) calculations. These methods, while precise, impose significant time and resource constraints, limiting their use in exhaustive parameter exploration. Moreover, these expensive simulations can contain variable errors over the large unknown parameter space, which needs to be quantified and propagated. Thus, predictive modelling is required to estimate the functional space accurately over scarcely sampled data with heteroskedastic noise, while preserving the physical relevance of the estimation. Therefore, we present a Physically Constrained Ensemble Gaussian Process (pc-EGP) framework designed to efficiently model complex and noisy quantum systems under physical consistency constraints. The proposed method first enforces physical constraints as a user controlled weighted penalty to the data-driven loss function of the Gaussian Process (GP) surrogates. Then an ensemble of such GP models is trained with variable noisy simulations via numerical quadrature method where these multiple GP(s) at different nodes is integrated as a quadrature weighted average. We first demonstrate the framework on synthetically generated data before applying to quantum systems. In the first case study, we leverage DMRG simulations of the Bose-Hubbard Model to predict the critical interaction parameter Uc governing the superfluid-to-Mott-insulator transition. In the second case study, we demonstrate our method on QMC simulations, of a quantum liquid confined inside a nanoporous silicate with the goal of optimizing a chemical environment to realize a one-dimensional superfluid. Compared to conventional GP, pc-EGP achieves a better balance of accuracy and physically meaningful predictions.

We introduce the fermionized time-dependent Hartree-Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by the exact evolutions, while maintaining a simple physical picture due to its mean-field nature.

We investigated the effects of Ni doping on carrier density and anomalous electrical transport properties in CeCo$_{1-x}$Ni$_x$In$_5$ ($x \leq 0.3$) by performing Hall resistivity measurements. The carrier density, estimated from the Hall coefficient $R_{\rm H}$ at a temperature of 0.5 K in high magnetic fields, increases linearly with $x$, indicating that the doped Ni ions act as electron dopants. In CeCoIn$_5$, the magnitude of $-R_{\rm H}$ is strongly enhanced at magnetic fields near the superconducting upper critical field $H_{c2}$ and in the low-field region above the superconducting transition temperature $T_c$. However, these anomalies are found to be significantly suppressed by Ni doping. Possible origins of this suppression in $-R_{\rm H}$ are discussed.

As a powerful theoretical construct, the entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system. From the EH, one can extract a variety of entanglement quantities, such as entanglement entropies, negativity, and the entanglement spectrum. However, its general analytical form remains largely unknown. While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited, especially when Lorentz invariance is absent. In this work, we propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods to numerically reconstruct the entanglement Hamiltonian in two-dimensional systems and systematically explore its applicability to systems without translational invariance, going beyond the original scope of the primordial Bisognano-Wichmann theorem. Various quantum phases--including gapped and gapless phases, critical points, and phases with either discrete or continuous symmetry breaking--are investigated, demonstrating the versatility of our method in reconstructing entanglement Hamiltonians. Furthermore, we find that when the entanglement boundary of a system is ordinary (i.e., free from surface anomalies), the LBW ansatz provides an accurate approximation well beyond Lorentz-invariant cases. Our work thus establishes a general framework for investigating the analytical structure of entanglement in the complex quantum many-body systems.

Strongly correlated molecules often contain dense manifolds of low-lying spin states, making total-spin symmetry essential for predictive electronic-structure theory. Neural-network quantum states provide flexible variational wavefunctions, but commonly used fermionic architectures do not enforce this symmetry and can therefore converge to spin-contaminated states with misleading energies and properties. Here we introduce a spin-adapted neural-network backflow (SA-NNBF) ansatz in second quantization, which combines configuration-dependent spatial orbitals with a compressed spin eigenfunction. A projected tensor compression scheme for spin eigenfunctions and a particle-hole representation make variational Monte Carlo calculations with SA-NNBF practical for active spaces containing more than one hundred electrons. Across hydrogen chains and iron-sulfur clusters, SA-NNBF eliminates spin contamination and consistently achieves lower variational energies than standard NNBF with a comparable number of parameters. For the CAS(113e,76o) active-space model of FeMoco, SA-NNBF yields a highly compact spin-adapted variational state, achieving an energy competitive with recent spin-adapted DMRG calculations at bond dimension $D=10000$ while using orders of magnitude fewer parameters. Our work establishes a general framework for developing spin-symmetry-preserving neural-network quantum states for chemically realistic strongly correlated electrons.

Two-dimensional Fermi liquids at low temperatures have been theoretically established to exhibit an odd-even effect in the collective quasiparticle relaxation rates where even-parity deformations of the Fermi surface decay at a much faster rate than odd-parity ones. A predicted consequence of this effect is a new tomographic transport regime that mixes hydrodynamic and collisionless transport. In the presence of a magnetic field, however, the tomographic regime is expected to evolve towards conventional transport regimes as soon as the cyclotron radius becomes smaller than the dominant odd-parity mean-free path. In this work, we examine this transition from the point of view of collective modes, using a numerically exact solution of the linearized Boltzmann equation within a generalized relaxation time approximation for the odd-parity and even-parity modes. In the absence of a magnetic field, the transverse conductivity exhibits two diffusive tomographic collective modes, and we find that at a critical magnetic field one of these two tomographic modes disappears. Which tomographic mode persists depends on the Landau parameters, and becomes increasingly dominated by hydrodynamic modes at high fields. We corroborate our analysis using a variational approach for the Fermi surface deformation that captures the angular structure of the deformation and the critical magnetic field strength. The collective modes discussed here can in principle be observed by examining the damping of longitudinal and transverse current responses in finite magnetic fields.

Large-spin two-dimensional magnets are generally expected to develop conventional long-range order once the dominant exchange scale becomes appreciable. The layered spin-$3/2$ maple-leaf compound Na$_2$Mn$_3$O$_7$ defies this expectation: despite sizable antiferromagnetic interactions and no evident disorder, it exhibits no magnetic ordering and displays two well-separated thermodynamic crossover scales. We show that this behavior originates from a crystallography-driven molecularization of the magnetic degrees of freedom. The low-symmetry structure partitions the Mn sublattice into inequivalent exchange pathways, generating a pronounced hierarchy that nearly isolates antiferromagnetic hexagons. Magnetic correlations therefore develop in two stages: first within individual hexagons at a scale set by the dominant exchange, and only at much lower temperatures do frustrated inter-hexagon couplings attempt to establish coherence across the lattice. While isolated hexagons reproduce the two-step thermodynamic structure, the experimentally relevant temperature scales emerge only once the hexagons are embedded in the frustrated two-dimensional network. The resulting quantum ground state is magnetically disordered, characterized by strong intra-hexagon correlations and rapidly decaying inter-hexagon correlations. These results identify crystallographic inequivalence as a materials-level mechanism for stabilizing molecularized and quantum-disordered states even in large-spin two-dimensional magnets.

We investigate the phase structure of the single-flavor Gross--Neveu model with Wilson fermions using the Grassmann corner transfer matrix renormalization group (CTMRG). The path integral is formulated as a two-dimensional Grassmann tensor network and approximately contracted by the Grassmann CTMRG algorithm. We investigate the phase diagram by varying the fermion mass and the four-fermion coupling, using the pseudoscalar condensate as an order parameter for the $\mathbb{Z}_{2}$ parity symmetry breaking phase. The universality classes of the phase boundaries are identified through the central charge $c$ obtained via scaling analysis of the entanglement entropy. Furthermore, we extract the quantity related to the entanglement spectrum from the converged CTMRG environments, allowing us to distinguish the topological insulator phase and the trivial phase. The resulting phase structure suggests that the Aoki phase is separated from the other phases by critical lines characterized by $c=1/2$, while the critical lines with $c=1$ separate the topological insulating and trivial phases. Our numerical results also indicate that the Aoki phase does not persist in the strong-coupling regime for the single-flavor theory.

Charge-$4e$ superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for topological charge-$2ne$ superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge-$2ne$ superconductors from charge-$2e$ ingredients, and by breaking the charge $U(1)$ symmetry in certain classes of quantum Hall states, in both spinless and spinful systems. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge-$2ne$ superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low-energy description of the topological charge-$2ne$ superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.

FeF$_2$ is a prototypical rutile antiferromagnet recently proposed as an altermagnet, with a magnetic symmetry that permits spin-split electronic bands and chiral magnons. Using very-high-resolution inelastic neutron scattering on a single crystal of FeF$_2$, we show that the dominant source of magnon splitting is in fact the long-range dipolar interaction rather than altermagnetic exchange terms. At momenta where the dipolar splitting vanishes, we observe additional broadening due to altermagnetic chiral splitting and estimate this splitting to be $\sim$35 $\mu$eV. Polarized measurements further reveal that, where dipolar splitting is present, the chiral magnon modes become mixed and the resulting modes are predominantly linearly polarized, with at most a small chiral component. These findings highlight the significant effect of dipolar interactions on magnon chirality, particularly when altermagnetic interactions are weak.

Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS and Migdal-Eliashberg theories. We consider the problem of obtaining closed-form analytical lower and upper bounds on transition temperatures for such systems. We focus mainly on a class of models known as the gamma-model, a variation of the Eliashberg theory of superconductivity where the effective interaction potential scales as V(Omega) proportional to 1/|Omega|^gamma. Building on a recent reformulation of Migdal-Eliashberg theory expressed as a classical infinite spin chain with nonlocal interactions [1,2], and employing a linear algebra analysis of the Hessian matrix obtained from the free energy functional, we derive rigorous, closed-form expressions for upper and lower bounds on the superconducting transition temperature for any gamma > 0. The main result of the paper is to establish an analytical upper bound on the transition temperature in closed form. Our upper bound is significantly tighter than those currently available in the literature and demonstrates rapid convergence toward results from prior numerical studies. Also, by applying the singularity condition directly to the unbounded Hessian matrix, our independently performed calculations confirm the lower bounds previously established in the literature [3].

We show that certain 't Hooft anomalies not detected by standard closed four-dimensional probes can become visible when a quantum field theory is placed on asymptotically locally Euclidean (ALE) spaces. As a concrete example, we use the Eguchi-Hanson (EH) space, whose defining features are its nontrivial second cohomology generated by the self-intersecting two-sphere and its asymptotic boundary $\mathbb{RP}^3$, which carries torsion and thus furnishes additional cohomological data absent on conventional backgrounds. For a theory with symmetry $G_1\times G_2$, we turn on background flux for $G_1$ and probe potential anomalies by performing a global $G_2$ transformation; the resulting anomaly is captured by a five-dimensional mapping torus. The anomaly receives contributions from the four-dimensional characteristic classes on EH space as well as from the $\eta$-invariant associated with the $\mathbb{RP}^3$ boundary. The anomaly detected in this way imposes additional constraints on asymptotically free gauge theories with fixed trivial asymptotic boundary conditions. In particular, infrared composite spectra that match anomalies on standard closed manifolds may nevertheless fail to reproduce the EH anomaly, and thus cannot by themselves furnish a complete symmetry-preserving infrared realization.

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the Néel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.