Bosonic excitations like phonons and magnons dominate the low-temperature transport of magnetic insulators. Similar to electronic Hall responses, the thermal Hall effect (THE) of charge-neutral bosons has been proposed as a powerful tool for probing topological properties of their wave functions. For example, the intrinsic contribution of the THE of a perfectly clean system is directly governed by the distribution of Berry curvature, and many experiments on topological magnon and phonon insulators have been interpreted in this way. However, disorder is inevitably present in any material, and its contribution to the THE has remained poorly understood. Here, we develop a rigorous kinetic theory of the extrinsic side-jump contribution to the THE of bosons. We show that the extrinsic THE is always relevant for bosonic systems and can be of the same order as the intrinsic one but sensitively depends on the type of local imperfection. We study different types of impurities and show that a THE can even arise as a pure impurity-induced effect in a system with a vanishing intrinsic contribution. As a side product, we also generalize existing results for the electronic anomalous Hall effect to general types of impurities beyond the standard assumption of local potential scattering. We discuss the importance of our results for the correct interpretation of THE measurements, for example, in the Kitaev magnet $\alpha \text{−}{\mathrm{RuCl}}_3$, and provide a ready-to-use formula for comparison to experimental data.

The local structure and chemical environment critically govern transport properties in quantum and energy materials, but their atomic-scale manifestations remain elusive. Here we uncovered the atomic characteristics, intrinsic origin, and thermoelectric implications of chemical inhomogeneity in ${\text{Bi}}_2{\text{Te}}_3$-based materials with varying Se alloying. Using aberration-corrected electron microscopy, chemical bonding analysis, and thermodynamic modeling, we revealed pronounced Se enrichment in the central layer of a quintuple structure and constructed precise atomic models for this intrinsic inhomogeneity. Atomic-scale charge-density and valence-state measurements provided direct experimental evidence for chemical bonding disparity in ${\text{Bi}}_2{\text{Te}}_3$, with more covalent bonding in central layers and greater ionic bonding in outer layers. We also showed that this bonding disparity, coupled with entropy-enthalpy competition, drove the observed site preference and local chemical segregation in ${\text{Bi}}_2{\text{Te}}_{3\text{−}x}{\text{Se}}_x$ ($x=0.5$, 1.0, 1.5, 2.0, and 2.5). The site-resolved bonding analyses further demonstrated that selective Se occupation tuned both ionic and covalent components of Bi–$X$ bonds in ${\text{Bi}}_2{\text{Te}}_{3\text{−}x}{\text{Se}}_x$. Therefore, this intrinsic chemical inhomogeneity modulated bonding polarity, the electronic band gap, and the Seebeck coefficient, serving as a fundamental determinant of thermoelectric performance. Our findings highlight atomic-scale chemical inhomogeneity as a key factor in tailoring functional properties of layered quantum materials beyond thermoelectrics.

Anderson localization is a quantum phenomenon in which disorder localizes electronic wave functions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the standard transfer matrix method, we extract the localization length from the modular density matrix in quasi-one-dimensional systems. This approach successfully captures the metal-insulator transition in the three-dimensional Anderson model and in the two-dimensional Anderson model with spin-orbit coupling. It can be also readily extended to multi-orbital systems. We further generalize the formalism to interacting systems, showing that the one-dimensional spinless attractive model exhibits the expected metallic phase, consistent with previous studies. More importantly, we demonstrate the existence of a two-dimensional metallic tendency in the presence of Hubbard interactions and disorder. This method offers a new perspective on Anderson localization and its interplay with interactions.

Hyperuniform particle arrangements are characterized by a local number variance within a spherical window of radius $R$ that grows more slowly than the volume of the window, i.e., $R^d$, in $d$-dimensional Euclidean space. We generalize this concept to describe the large-scale behavior of particle systems in which particles carry weights: internal degrees of freedom such as scalars (charges and masses), vectors (electric dipole moments, velocities, and torques), pseudovectors (spins and angular momenta), directors (bond orientations), tensors (quadrupole moments), or extrinsic local attributes (Voronoi-cell characteristics). The underlying hyperuniform arrangement may be ordered (crystals and quasicrystals) or disordered, the latter of which has been extensively studied for its novel properties. Our generalization extends hyperuniformity from fluctuations in particle positions to fluctuations in the spatial distribution of weights and examines how weighted fluctuations compare to their unweighted counterparts. We derive generalized weighted pair correlation functions, autocovariance functions, and spectral functions and show their relation to formulas for the local variance in weighted many-particle systems. Then, we apply our formalism to determine the hyperuniformity or nonhyperuniformity of bond-orientational ordered phases, dipolar liquid water, Voronoi-cell volumes, and certain ionic liquids in various Euclidean space dimensions. We demonstrate that hyperuniformity in the particle system does not necessarily translate to hyperuniformity of the weighted system. In fact, cases exist where a hyperuniform particle system becomes antihyperuniform when weighted and others where nonhyperuniform or antihyperuniform particle systems yield hyperuniform weighted systems. This theoretical framework provides a road map for quantifying large-scale fluctuations in weighted many-particle systems, offering a powerful tool for identifying systems with novel physical properties.

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of $N=0$ and $N=1$ orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at $\nu =\frac{1}{3}$ and a reentrant integer quantum Hall state at $\nu =\frac{7}{3}$. On the $N=0$ side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the $N=1$ transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the $N=0$ levels, suggesting a paired composite fermion state stabilized by Landau level mixing.

One of the hallmarks of topological systems is the robust quantization of particle transport. It is the origin of the integer-valued quantum Hall conductivity and a potential tool for quantum information technology. Recent experiments on topological pumps constructed by using arrays of photonic waveguides and described by the (lattice-translational invariant) Aubry-André-Harper model, have demonstrated both integer and fractional transport of lattice solitons. In these systems, a background medium mediates interactions between photons via a Kerr nonlinearity and leads to the formation of self-bound multiphoton states. Upon increasing the interaction strength, a sequence of transitions was observed from a phase with integer transport in a pump cycle through different phases of fractional transport to a phase with no transport. We here present a quantum description of topological pumps of self-bound many-particle states in terms of an effective Hamiltonian of their center-of-mass (c.m.) motion, which allows one to introduce an effective band structure $E_{\mu }(K)$ with $K$ being the c.m. momentum and to classify topological phases in terms of generalized symmetries. We provide an explicit analytic expression of the effective Hamiltonian for few particles in the strong interaction limit and present numerical results in the more general case. We identify a topological invariant, an effective single-particle Chern number, which fully governs the soliton transport. Increasing the interaction strength in the Aubry-André-Harper model leads to a successive merging of c.m. bands, which is the origin of the observed sequence of topological phase transitions and also the potential breakdown of topological quantization for some interaction strength.

Understanding universal aspects of many-body systems is one of the central themes in modern physics. Recently, the stabilizer Rényi entropy (SRE) has emerged as a computationally tractable measure of nonstabilizerness, a crucial resource for fault-tolerant universal quantum computation. While numerical results suggested that the SRE in critical states can exhibit universal behavior, its comprehensive theoretical understanding has remained elusive. In this work, we develop a field-theoretical framework for the SRE in a ($1+1$)-dimensional many-body system and elucidate its universal aspects by using boundary conformal field theory. We demonstrate that the SRE is equivalent to a participation entropy in the Bell basis of a doubled Hilbert space, which can be calculated from the partition function of a replicated field theory with the interlayer line defect created by the Bell-state measurements. This identification allows us to characterize the universal contributions to the SRE on the basis of the data of conformal boundary conditions imposed on the replicated theory. We find that the SRE of the entire system contains a universal size-independent term determined by the noninteger ground-state degeneracy known as the $g$ factor. In contrast, we show that the mutual SRE exhibits the logarithmic scaling with a universal coefficient given by the scaling dimension of a boundary-condition-changing operator, which elucidates the origin of universality previously observed in numerical results. As a concrete demonstration, we present a detailed analysis of the Ising criticality, where we analytically derive the universal quantities at arbitrary Rényi indices and numerically validate them with high accuracy by employing tensor-network methods. These results establish a field-theoretical approach to understanding the universal features of nonstabilizerness in quantum many-body systems.

Light-induced quantum phases offer the potential for simple and powerful tuning of material properties. For example, simply illuminating 2D materials in the integer quantum Hall regime with polarized light is predicted to drive quantum phase transitions. Such phenomena are largely beyond the current frontier of solid state experiments due to technical limitations on laser intensity and material purity. However, the Harper-Hofstadter mapping which relates a two-dimensional integer quantum Hall system to a 1D quasicrystal enables the same polarization-dependent light-induced phase transitions to be observed using a quantum gas in a driven quasiperiodic optical lattice. We report results of such an experiment. We observe an interlaced phase diagram of localization-delocalization phase transitions as a function of drive polarization and amplitude. Elliptically polarized driving can stabilize an extended critical phase featuring multifractal wave functions; we observe signatures of this phenomenon in anomalous polarization-dependent subdiffusive transport. In this regime, increasing the strength of the quasiperiodic potential can enhance rather than suppress transport. These experiments demonstrate a simple method for synthesizing exotic multifractal states and exploring light-induced quantum phases across different dimensionalities.

Spin waves (magnons) in two-dimensional (2D) materials have received increasing interest due to their unique states and potential for tunability. However, many interesting features of these systems, including Dirac points and topological states, occur at high frequencies, where experimental probes are limited. Here, we study a crystal formed by patterning a hexagonal array of holes in a perpendicularly magnetized thin film. Through simulation, we find that the magnonic band structure imitates that of graphene, but additionally has some kagomelike character and includes a few flat bands. Surprisingly, its nature can be understood using a nine-band tight-binding Hamiltonian. This clear analogy to 2D materials enables band-gap engineering in 2D, topological magnons along 1D phase boundaries, and spectrally isolated modes at 0D point defects. Interestingly, the 1D phase boundaries allow access to the valley degree of freedom through a magnonic analog of the quantum valley Hall insulator. These approaches can be extended to other magnonic systems, but are potentially more general due to the simplicity of the model, which resembles existing results from electron, phonon, photon, and cold-atom systems. This finding brings the physics of spin waves in 2D materials to more experimentally accessible scales, augments it, and outlines a few principles for controlling magnonic states.

The high complexity of many-body quantum dynamics means that essentially all analytical or numerical approaches either exploit special structure or are approximate in nature. One such approach—the memory function formalism—involves a carefully chosen split into “fast” and “slow” modes. An approximate model for the fast modes can then be used to solve for Green’s functions $G(z)$ of the slow modes, and the success of this approach depends on the accuracy of the fast space approximation. Using a formulation in operator Krylov space known as the recursion method, we prove the emergence of a universal random matrix description of the fast mode dynamics. This is captured by the “level-$n$ Green’s function” $G_n(z)$, which we show approaches universal scaling forms in the “fast limit” $n\to \infty$. Notably, this emergent universality can occur in both chaotic and nonchaotic systems, provided their spectral functions are sufficiently smooth. This universality of $G_n(z)$ turns out to be precisely analogous to the universality of eigenvalue correlations in random matrix theory (RMT), even though there is no explicit randomness present in the Hamiltonian. Concretely, at finite $z$ we show that $G_n(z)$ approaches the Wigner semicircle law, while if $G(z)$ is the Green’s function of certain hydrodynamical variables, we show that at low frequencies $G_n(z)$ is instead governed by the Bessel universality class from RMT. As an application of this universality, we give a new numerical method, the spectral bootstrap, for approximating spectral functions, including hydrodynamic transport data, from a finite number of Lanczos coefficients. Our proof involves a map to a Riemann-Hilbert problem which we solve using a steepest-descent-type method, rigorously controlled in the $n\to \infty$ limit. Via the steepest-descent procedure, we are led to a related Coulomb gas optimization problem, and we discuss how a recent conjecture—the “Operator Growth Hypothesis”—implies that chaotic operator dynamics can generically be identified with the critical point of a confinement transition in this Coulomb gas. These results elevate the recursion method from a useful numerical technique to a theoretically principled framework with universal content.

We investigate quantum transport in micrometer-sized single crystals of ${\mathrm{Bi}}_4{\mathrm{Br}}_4$, a material predicted to be a second-order topological insulator. 1D topological states with long phase coherence times are revealed via the modulation of quantum interference with magnetic field and gate voltage. In particular, we demonstrate the existence of Aharonov-Bohm interference between 1D ballistic states several micrometers long, that we identify as phase-coherent hinge modes on neighboring step edges at the crystal surface. These Aharonov-Bohm oscillations are made possible by a disordered phase-coherent contact region, the existence of which is confirmed by scanning transmission electron microscopy combined with energy-dispersive x-ray spectroscopy (STEM-EDX) of FIB lamellae. Their coherent nature modulates the transmission of the 1D edge states, leading to weak antilocalization and universal conductance fluctuations with surprisingly large characteristic fields and a strongly anisotropic behavior. These complementary experimental results provide a comprehensive, coherent description of quantum transport in ${\mathrm{Bi}}_4{\mathrm{Br}}_4$ and establish the material as a second-order topological insulator with topologically protected 1D ballistic states.

Superconductivity arises from the global phase coherence of Cooper pairs. Modulation of phase coherence leads to quantum phase transitions, serving as an important tool for studying unconventional superconductivity. Here, we demonstrate bosonic phases across the superconductor-insulator transition in infinite-layer nickelate superconducting films by the control of spatially periodic network patterns. Magnetoresistance oscillations with a periodicity of $h/2e$ provide direct evidence of $2e$ Cooper pairing in nickelates. The phase transition is predominantly driven by enhanced superconducting fluctuations, and Cooper pairs are involved in charge transport across the transition. Notably, we observe two types of anomalous metallic phases, emerging, respectively, at finite magnetic fields and down to zero magnetic field. They can be characterized by bosonic excitations, suggesting the dynamic roles of vortices in the ground states. Our work establishes nickelates as a key platform for investigating the rich landscape of bosonic phases controlled via the phase coherence of Cooper pairs.

’t Hooft anomalies of global symmetries play a fundamental role in quantum many-body systems and quantum field theory (QFT). In this paper, we make a systematic analysis of lattice anomalies—the analog of ’t Hooft anomalies in lattice systems—for which we give a precise definition. Crucially, a lattice anomaly is not a feature of a specific Hamiltonian but rather is a topological invariant of the symmetry action. The controlled setting of lattice systems allows for a systematic and rigorous treatment of lattice anomalies, shorn of the technical challenges of QFT. We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways but also have crucial differences. In particular, lattice anomalies and QFT anomalies are not, contrary to a common expectation, in one-to-one correspondence, and there can be nontrivial anomalies on the lattice that are infrared (IR) trivial: They admit symmetric trivial gapped ground states and map to trivial QFT anomalies at low energies. Nevertheless, we show that lattice anomalies (including IR-trivial ones) have a number of interesting consequences in their own right, including connections to commuting projector models, phases of many-body-localized systems, and quantum cellular automata. We make substantial progress on the classification of lattice anomalies and develop several theoretical tools to characterize their consequences on symmetric Hamiltonians. Our work places symmetries of quantum many-body lattice systems into a unified theoretical framework and may also suggest new perspectives on symmetries in QFT.

Chiral superconductors have long been theorized to break time-reversal symmetry and support exotic topological features such as Majorana modes and spontaneous edge currents, promising ingredients for quantum technologies. Although several unconventional superconductors may exhibit time-reversal symmetry breaking, clear microscopic evidence of chiral pairing has remained out of reach. In this work, we demonstrate direct real-space signatures of chiral superconductivity in a single atomic layer of tin on Si(111). Using quasiparticle interference imaging, we detected symmetry-locked nodal and antinodal points in the Bogoliubov quasiparticle wave function, tightly bound to atomic point defects in the tin lattice. These nodal features, along with their surrounding texture, form a distinct real-space pattern exhibiting a clear and exclusive hallmark of chiral superconductivity. Our findings, reinforced by analytical theory and numerical simulations, offer unambiguous evidence of chiral pairing in a two-dimensional material.

The fidelity of operations on a solid-state quantum processor is fundamentally bounded by environmental decoherence. Characterizing environmental fluctuations is challenging because the acquisition time of nonadaptive experimental protocols limits temporal precision and can average out rapid features of the underlying dynamics. Here, we overcome this temporal-resolution limit by 2 orders of magnitude using a field-programmable gate-array powered classical controller that adaptively and continuously tracks the relaxation-time fluctuations of two fixed-frequency superconducting transmon qubits, which exhibit average relaxation times of approximately 0.17 ms and occasionally exceed 0.5 ms. We report events in which the relaxation time switches by nearly an order of magnitude over timescales of just tens of milliseconds, rather than minutes or hours as previously reported. Our real-time Bayesian estimation protocol estimates relaxation times within a few milliseconds, close to the decoherence timescale itself. Our statistical analysis further suggests that some of these fast fluctuations arise from two-level systems switching at rates up to 10 Hz, 4 orders of magnitude faster than earlier reports. These results redefine the timescales relevant for calibration in superconducting quantum processing units, establish a reference for rapid relaxation-rate characterization in device screening, and improve our understanding of fast relaxation dynamics.

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

The Yang-Lee universality class arises when an imaginary magnetic field is tuned to its critical value in the paramagnetic phase of the $d<6$ Ising model. In $d=2$, this nonunitary conformal field theory (CFT) is exactly solvable via the $M(2,5)$ minimal model. As found long ago by von Gehlen using exact diagonalization, the corresponding real-time, quantum critical behavior arises in the periodic Ising spin chain when the imaginary longitudinal magnetic field is tuned to its critical value from below. Even though the Hamiltonian is not Hermitian, the energy levels are real due to the $\mathcal{PT}$ symmetry. In this paper, we explore the analogous quantum critical behavior in higher-dimensional non-Hermitian Hamiltonians on regularized spheres $S^{d-1}$. For $d=3$, we use the recently invented, powerful fuzzy sphere method, as well as discretization by the platonic solids cube, icosahedron, and dodecahedron. The low-lying energy levels and structure constants we find are in agreement with expectations from the conformal symmetry. The energy levels are in good quantitative agreement with the high-temperature expansions and with Padé extrapolations of the $6-\epsilon$ expansions in Fisher’s $i{\varphi }^3$ Euclidean field theory for the Yang-Lee criticality. In the course of this work, we clarify some aspects of matching between operators in this field theory and quasiprimary fields in the $M(2,5)$ minimal model. For $d=4$, we obtain new results by replacing $S^3$ with the self-dual polytope called the 24-cell.

In this work, we demonstrate a remarkable field-induced ferroquadrupolar phase emanating from the magnetoelastic coupling. Using synchrotron x-ray and neutron diffraction, heat capacity measurements, as well as mean-field modeling, we show that above the critical magnetic field, ferroquadrupolar $O_2^{-2}$ order is stabilized as the main order parameter, in competition with the field-induced magnetic polarization. This is revealed by a severe lattice distortion and the suppression of antiferromagnetic ordering of the dipole moments. Even in zero magnetic field, the previously reported antiferromagnetic order is a mixed quadrupolar-dipolar phase, further highlighting the crucial role of spin-lattice interactions. This complete understanding of the magnetoelastic phase diagram establishes ${\mathrm{TbPO}}_4$ as a model system for studying nematic-antiferromagnetic transitions and provides key Hamiltonian parameters for its description.

The interplay between symmetry and topological properties plays a very important role in modern physics. In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems. Very recently, the concept of SET phases has been generalized into fermionic systems and their corresponding classification schemes are also proposed. Nevertheless, how to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem. In this paper, we first construct exactly solvable models for nonanomalous nonchiral $2+1\mathrm{D}$ fSET phases, namely, the symmetry-enriched fermionic string-net models, which are described by commuting-projector Hamiltonians whose ground states are the fixed-point wave functions of each fSET phase. Mathematically, we provide a partial definition to $G$-graded super fusion category (when the total symmetry $G^f$ is a direct product of physical symmetry $G$ and fermion-parity symmetry ${\mathbb{Z}}_2^f$), which is the input data of a symmetry-enriched fermionic string-net model. Next, we construct exactly solvable models for nonchiral $2+1\mathrm{D}$ fSET phases with ’t Hooft anomaly, especially the $H^3(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly which is different from the well-known bosonic $H^4[G,U(1{)}_T]$ anomaly. In our construction, this $H^3(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly is characterized by a violation of fermion-parity conservation in some of the surface $\mathcal{F}$ moves (a type of renormalization moves for the ground state wave functions of surface fSET phases), and also by a new fermionic obstruction $\mathrm{\Theta }$ in the surface pentagon equation. We demonstrate this construction in a concrete example that the surface topological order is a ${\mathbb{Z}}_4$ gauge theory embedded into a fermion system and the total symmetry $G^f={\mathbb{Z}}_2^f\times {\mathbb{Z}}_2\times {\mathbb{Z}}_4$. We further conjecture that the $H^2(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly is characterized by a possible violation of nonterminating $q$-type (called $\sigma$-type) string in the fusion rules of surface models.

Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies: one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy, and the other, angle-resolved photoemission spectroscopy (ARPES). We combine these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fermion model (TCFM) representing electron fractionalization succeeds in reproducing various detailed features of these experimental data: ARPES and QPI data are concomitantly reproduced by the TCFM in full energy and momentum spaces. The measured QPI pattern reveals a signature characteristic of the TCFM, distinct from the conventional single-component prediction, supporting the validity of the electron fractionalization in the cuprates. The integrated analysis also solves the puzzles of ARPES and QPI data that are seemingly inconsistent with each other. The overall success of the TCFM offers a comprehensive understanding of the electronic structure of the cuprates, in particular, the unoccupied side of the spectra, of which momentum-resolved structure has long been unexplored experimentally. We further predict that a characteristic QPI pattern should appear in the unoccupied high-energy part if the fractionalization is at work. We propose that integrated-spectroscopy analyses offer a promising way to explore challenging issues of strongly correlated electron systems.