Papers

The superconducting diode effect (SDE) is a fascinating nonreciprocal phenomenon where the critical current is different for opposite current directions. It is widely believed that realizing SDE requires breaking both inversion symmetry (IS) and time-reversal symmetry (TRS), which are usually achieved via heterostructure engineering and applying external magnetic fields. Here, we report a pressure-induced magnetic-field-free SDE in NbSe2 flakes without any heterostructures. We show that pressure alone breaks the IS, as confirmed by the second harmonic generation. Crucially, upon applying an out-of-plane magnetic field (B), the SDE exhibits even-in-B behavior, implying the absence of explicit TRS breaking. This finding challenges the prevailing theoretical paradigm and demonstrates that a magnetic-field-free SDE can emerge without explicitly breaking TRS. Thereby, our work establishes pressure engineering as a powerful tool for inducing nonreciprocal superconductivity and designing versatile, magnetic-field-free superconducting devices.

The intrinsic electronic structures of narrow bandgap thermoelectric (TE) materials serve as a platform for the investigation of coupling effects of quasi-particles under high pressure, enabling the exploration of emerging electronic and phonon transport, superconductivity, and topological transition. Here, we report the discovery of pressure-induced superconductivity in the TE semiconductor Mg3Sb2. Upon the increased pressure, the metallization occurs at 8.7 GPa, followed by a superconducting transition concomitant with a carrier-type crossover from p- to n-type. This phenomenon arises from a pressure-induced structural phase transition from the semiconducting P-3m1 to the metallic C2/m-I phase. The superconducting critical temperature (Tc) exhibits a dome-shaped pressure dependence, peaking at 3.3 K at 12.6 GPa. Combined theoretical calculations, high-pressure Raman spectroscopy, and X-ray diffraction (XRD) measurements reveal an additional structural transition above 20 GPa, yielding a distinct C2/m-II phase. Our findings establish the high-pressure phase diagram of Mg3Sb2, elucidate its pressure-dependent electronic properties, and provide valuable insights for future investigations of TE materials under high pressure.

When an electron-doped layer is stacked with a hole-doped layer with approximately equal carrier density, inter-layer Coulomb interaction turns the bilayer system into an exciton condensate (EC). In this Letter, we reveal a fundamental property of bilayer ECs: the excitonic order gives rise to nontrivial hidden quantum geometric effects in the correlated electron-hole bands, even when the non-interacting bands are trivial. Such peculiar EC-driven quantum geometry manifests itself in a characteristic out-of-plane polarization response upon applying an in-plane AC electric field to the bilayer EC system. In particular, the second-order response exhibits a characteristic inverse square scaling with the bilayer EC order parameter. Our finding reveals a fundamental hidden Berry phase effect driven by electron-hole correlations, and establishes bilayer EC as a promising platform for rich nonlinear physics.

We investigate superconductivity in a doped Kitaev quantum spin liquid by applying the many-variable variational Monte Carlo method to the hole-doped $t$-$J$-type Kitaev model. Using a projected pair-product wave function that can exactly represent the Kitaev quantum spin liquid, we examine the stability of superconducting phases on isotropic two-dimensional clusters. For the ferromagnetic Kitaev interaction, robust triplet $p$-wave superconductivity coexists with ferromagnetism in the low-to-intermediate doping regime but is suppressed as the system approaches the fully polarized ferromagnetic phase. For the antiferromagnetic Kitaev interaction, superconductivity exhibits a change in the dominant pairing symmetry from spin-dependent triplet $p$-wave at low doping to singlet $d+id$ at intermediate doping. By varying the strength of the ferromagnetic Kitaev interaction at fixed doping, we show that the triplet superconductivity increases together with the ferromagnetic moment and becomes strongest slightly below full polarization. Our results provide a theoretical basis for experimental searches for unconventional superconductivity, such as triplet superconductivity coexisting with ferromagnetism, in carrier-doped Kitaev candidate materials.

Photoemission spectroscopy on high $T_c$ superconductors find a puzzling nodal self-energy with $\omega/T$ scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions $V_{\alpha}(r) \sim 1/r^\alpha$, where a continuously doping-dependent exponent $1 \le \alpha \le 3$ interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate $\Gamma(\omega,T) \propto T^{\gamma} \Phi(\omega/T)$ in energy $\omega$ and temperature $T$, with $\gamma = 2-\frac{1}{\alpha}$ for nonlocal $ 1 < \alpha < 2$. Our results naturally capture the optimally doped to overdoped regimes, whereas the underdoped regime is qualitatively distinct. In our theory, spectroscopy-fitted exponents directly probe the charged fluid's effective spatial nonlocality, providing a way to falsify the theory by comparing photoemission spectroscopy against electron energy loss spectroscopy. More broadly, nonlocality cautions us to not immediately infer quantum critical phenomena when $\omega/T$ scaling is experimentally observed.

Exotic nanoparticle superstructures can be accessed by harnessing nanoparticle softness and charge regulation, features often viewed as obstacles to structural control. Here, we show that regulated charge mismatch in polymer-grafted nanoparticles enables the assembly of high-stoichiometry cubic superlattices. By co-tuning grafting density, particle size, and bulk composition, we realize ionic-lattice analogues such as CaF2 and Th3P4, as well as single-component A3 and A7 superlattices without atomic counterparts. The A3 lattice has recently been identified theoretically as a photonic band-gap lattice. These phases emerge from a 1:1 "parent" lattice when local charge neutrality cannot be satisfied, driving either progressive interstitial filling or reorganization into a larger basis. For instance, the systematic occupation of ZnS tetrahedral sites yields CaF2, while ligand-swapping symmetry breaking converts CsCl into Th3P4. Upon heating, the assemblies exhibit reversible lattice contraction and pronounced negative thermal expansion. Furthermore, the energetic penalty for defects increases with nanoparticle size, facilitating the scalable production of high-quality, open superlattices for photonic applications.

We present a comprehensive framework for investigating the optical response of metals from first principles that combines density functional theory, many-body perturbation theory, and efficient interpolation techniques based on maximally localized Wannier functions, and apply it to analyze the optical properties of silver (Ag), gold (Au), and copper (Cu). We evaluate the optical properties of these metallic materials considering both single-particle direct and phonon-assisted excitations, as well as the resistive Drude contribution. We find an overall excellent agreement with experimental optical measurements for these materials, and show that both single-particle and collective excitations are important in capturing their optical response in the infrared. Our methodology provides fundamental understanding of the optical response of metals and is generally applicable to investigate the optoelectronic properties of emerging metallic materials.

Neural networks can be studied not only as parameterized computational models but also as probability distributions over functions. In this paper we develop a Wilsonian interpretation of criticality in the neural network-quantum field theory correspondence, treating the infinite width Gaussian-process limit as a free field fixed point and finite width corrections as perturbations that create non-Gaussian interactions. In this way, we do not see the departure from infinite width as a small approximation error but as the process by which interaction, complexity, expressivity and phase-like behaviour enter neural network function space. Width, depth, activation nonlinearity, initialization variance, and training dynamics are considered as control parameters that change the effective action of the network ensemble. The critical regime is when the higher-order connected correlation functions become non-negligible, and when the finite width operators become relevant or marginal scaling factors, and when the function distribution becomes sensitive to scale-dependent structure. There we can view overparameterization as suppressing a relationship of interacting terms and we find that the critical structure of finite neural networks is given by finite-width effects. This framework is a theoretical basis for studying trainability, generalization, and architectural universality of neural network functions through Wilsonian fixed points, perturbations, and critical surfaces.

Magnetic components in high-frequency, high-power-density converters are increasingly driven by non-sinusoidal flux-density waveforms with fast transitions, minor-loop operation, dc bias, and temperature variation. Under these conditions, steady-state core-loss formulas and single-valued material curves cannot fully capture transient magnetization responses. This work proposes the Physics-Informed Hybrid Neural Operator (PI-HNO), a compact material-specific neural model with B-H energy-consistency regularization for core-loss-oriented transient magnetization prediction. Given the measured B(t)-H(t) history, the input B(t) series over the prediction interval and operating-condition information, PI-HNO predicts the H(t) series and the corresponding reconstructed B-H trajectory. The model integrates a local recurrent branch for boundary-state representation and rate-dependent response evolution with a Preisach-inspired global branch that extracts waveform-level hysteresis context. Evaluation on the MagNetX transient database using material-specific models for 14 ferrite materials demonstrates that PI-HNO achieves a compact trade-off between sequence accuracy and B(t)-H(t) energy consistency, with the mean and 95th percentile B(t)-H(t) energy consistency errors of 1.92% and 7.60%, respectively, using only 4777 trainable parameters per model. Ablation studies further demonstrate that the local, global, and energy-aware regularized components provide distinct contributions to transient magnetization prediction.

The synchronization and phase-locking behavior of oscillators with smooth dynamics is well captured by continuous phase-models à la Kuramoto. However, these models do not apply seamlessly for hybrid oscillators, where discrete events occur along their otherwise smooth dynamics. Consequently, the synchronization and phase-locking mechanisms of hybrid oscillators remain overlooked. Here, we combine experiments, theory, and simulations, to investigate and rationalize the coherent motion of pairs of hybrid oscillator. Using contact-charge electrophoretic (CCEP) oscillators as an experimental realization, we show that in-phase oscillations can occur, despite oscillators repelling each other. We rationalize this behavior by introducing a discrete-time framework that explicitly accounts for discrete events and elucidates the origin of phase-locking. Our model highlights the roles played by inertia and the decay of interaction strength along the oscillation cycle in promoting phase-locking of CCEP oscillators. More generally, it provides a phase-locking criterion that holds for a broader class of coupled hybrid oscillators, and reveals that various mechanisms can lead to their coherence.

Altermagnets combine compensated antiferromagnetic order with momentum-dependent spin splitting, offering a promising platform for spintronic applications without macroscopic magnetization or stray magnetic fields. Although a wide range of three-dimensional (3D) materials have been identified as altermagnets, two-dimensional (2D) altermagnets remain comparatively limited. In this work, we perform a high-throughput computational search for altermagnetism across 2710 materials in the Materials Cloud 2D Crystals (MC2D) database. Our approach combines symmetry-based screening with first-principles density functional theory calculations, including self-consistent Hubbard-$U$ corrections, to reliably capture magnetic ground states. Through a systematic exploration of magnetic configurations and their energetic stability, we identify 42 materials exhibiting altermagnetic ground states for at least one value of $U$, of which 24 remain robust upon determination of the Hubbard-$U$ parameters from first principles–including 4 materials previously reported in the literature and 20 newly predicted candidates. These comprise promising monolayers such as metallic Fe$_2$Si$_2$SbO$_9$, and insulating CoBrO, with spin splittings about 294 meV and 330 meV, respectively. Our results significantly expand the pool of potential 2D altermagnet candidates with favorable exfoliation energetics and provide valuable guidance for experimental efforts. In addition, this work establishes a high-throughput computational framework for reproducible discovery and characterization of altermagnetic materials.

We numerically analyze chaos and diffusion in experimentally-relevant models of twisted bilayer graphene. Our results indicate that finite systems at both commensurate and incommensurate rotation angles exhibit chaos. We compute the Thouless energy of the system at intermediate twist angles to further understand the diffusive processes associated with the chaotic nature of the spectrum. We find that the mean free path of the non-interacting electrons scales with the system size, which is consistent with diffusive processes caused by border-induced scattering. In summary, our results show the role of borders as a experimentally relevant single-particle scattering mechanism, which is much stronger than in single-layer graphene and induces chaos and diffusion regardless of the rotation angle and the lattice commensurability.

We study simple inhomogeneous deformations of known two-dimensional classical lattice models described by conformal field theory (CFT) at large distances. The deformations are chosen to vary slowly at lattice scales, while preserving critical behavior. Globally, we find that such systems are described by a CFT in curved space, and identify the underlying space metric. Our two examples are the Ising model and the six vertex model with domain wall boundary conditions. In the latter boundaries are also inhomogeneous, which complicates the analysis. We nevertheless solve the free case using hydrodynamics. In the presence of interactions we determine the arctic curve which separates a critical fluctuating region from an ordered (frozen) phase.

Symmetry is fundamental to photonic systems. External (spatial) symmetries and internal symmetries—Lorentz reciprocity, energy conservation, and time-reversal symmetry—constrain the electromagnetic response. Photonic systems can also possess compound symmetries that combine external and internal transformations, exemplified by parity-time (PT) symmetry. However, a unified framework for general compound symmetries involving reciprocity, energy conservation, and time reversal remains lacking, leaving their classification and physical implications unexplored. In this paper, we present such a framework for linear photonic systems. We define compound transformations and symmetries, and derive their constraints on electromagnetic fields and scattering matrices. We show that internal, external, and compound symmetries are naturally described by the theory of double antisymmetry groups. This theory classifies linear time-invariant photonic systems into twelve symmetry categories, each imposing characteristic constraints on the electromagnetic response. We illustrate two representative categories with numerical examples of photonic crystal slabs and apply the theory to examine Kirchhoff's law of thermal radiation for a gyrotropic sphere. Our work provides a systematic foundation for analyzing and engineering symmetry in photonic systems.

Bernal-stacked bilayer graphene (BLG) hosts correlated electronic phases tied to low-energy Lifshitz transitions at saddle points in its valence band. To access this regime, ultralow charge disorder and control over a vertical electric field are simultaneously required. Here, we employ a twist-decoupled monolayer (MLG) to bias a proximal BLG in the absence of an external displacement field (D). We thereby reveal three-fold degenerate quantum Hall states at D = 0, with multiple transitions driven by doping, magnetic and electric field. Spontaneous broken symmetry in the vicinity of the valence band edge is signaled by the emergence of quantum oscillations with anomalous frequencies and large quasiparticle mass. These results indicate that electronic interactions in BLG are preserved in presence of an atomically close MLG, while showcasing the potential of CVD-grown graphene multilayers for the exploration of correlated phases of matter.

The discovery of next-generation energy-storage materials is increasingly limited by the complexity of the underlying design problem rather than by computational capability alone. Porous transition-metal oxides represent a particularly challenging class of battery materials because their performance emerges from coupled interactions among crystal chemistry, pore architecture, ion transport, electrochemistry, electro-chemo-mechanics, synthesis, manufacturing, and battery-system operation. Recent advances in generative artificial intelligence (AI) have demonstrated remarkable capabilities for generating chemically plausible crystal structures. However, current approaches remain largely focused on crystallographic validity and thermodynamic stability. This perspective presents a roadmap for advancing generative AI beyond crystal generation toward physics-informed, application-aware, and synthesis-aware inverse design. Using porous oxide electrodes as a representative materials platform, we propose a seven-tier physics-informed inverse-design framework integrating chemistry, thermodynamics, transport, electrochemistry, durability, cell compatibility, and manufacturability. We further identify the "Missing Data Problem" as a fundamental bottleneck limiting application-aware AI and introduce an autonomous knowledge-generation framework supported by a Porous Oxide Energy Materials Ontology and a continuously evolving "Knowledge Base". Together, these concepts establish the foundation for Synthesis-Aware, Closed-Loop Autonomous Discovery, providing a general framework for AI-enabled autonomous materials discovery across energy-storage materials and other functional materials.

In low density systems with strong interactions electrons are expected to crystallize into a Wigner solid. Recently, advances in two-dimensional systems where electrons carry Berry curvature have added a topological dimension to Wigner crystallization. Using a model for pseudospin interactions in a topological Wigner crystal, here we show that the competition between ferromagnetic Heisenberg exchange $J$ and the chiral interaction $\gamma$ on the triangular lattice stabilizes a zero-field skyrmion crystal whose density is continuously tunable through the ratio $\gamma/J$. The chiral interaction originates from finite Berry curvature in an underlying time-reversal broken Wigner crystal. In the continuum limit, the chiral interaction acts as a chemical potential for skyrmions, while higher-order gradient terms beyond the nonlinear sigma model select the skyrmion density. At large chiral coupling, we uncover a 24-site tetra-skyrmion crystal carrying four units of topological charge per magnetic unit cell, which becomes degenerate with four-sublattice tetrahedral order as $J \to 0$. We characterize the magnon structure for these phases and discuss the transition between the tunable skyrmion crystal to these states at large $\gamma/J$. Our results establish the phase diagram of ferromagnetic topological Wigner crystals.

We consider the problem of Coulomb drag in interactively coupled quantum circuits built of adiabatic constrictions: quantum point contacts and short quantum-wire channels. The interplay of spatial confinement and magnetic field leads to a rich oscillatory response of the drag current as a function of gate voltage and magnetic field: drag peaks track the depopulation of magnetoelectric subbands, are asymptotically periodic in inverse field, and their visibility is controlled by the competition of temperature with the field-sharpened tunneling width of the constriction. We derive a closed expression for the linear drag conductance whose interaction kernel simplifies dramatically in the experimentally relevant limit of a long thermal length compared with the range of the interwire coupling, investigate the drag in the nonlinear regime, where the drag current measures the transconductance of the drive channel at any field, and discuss physically motivated models of dissipation-induced nonreciprocity of the drag signal. Extensions accounting for Zeeman splitting, interaction renormalization of the barrier transmission, backscattering at high field, and the frequency structure of the circuit coupling delineate how each mechanism imprints itself on the temperature dependence and lineshapes of the drag oscillations.

Image formation in transmission electron microscopy (TEM) is governed by the coherent evolution of the electron wavefunction through the specimen and the objective lens. This physics maps naturally onto the gate model of quantum computation. We present QuScope, an open-source Python framework that expresses the complete TEM image-formation pipeline as quantum circuits. The $N\times N$ electron wavefunction is amplitude-encoded in $2\log_2 N$ qubits, and every optical element, including phase-grating transmission, Fresnel propagation between specimen slices, and the aberrated objective lens, is implemented as a diagonal unitary conjugated by quantum Fourier transforms. On this foundation, QuScope v0.2.0 implements validated imaging pipelines, covering conventional TEM under the phase-object approximation, full multislice CTEM and STEM for thick specimens. All quantum results reported here come from exact, noise-free statevector simulation of the circuits on classical hardware, and every result is validated against a classical twin implementation. Quantum and classical multislice exit waves agree to unit fidelity, and all physical constants are verified against standard references. We provide transpiled quantum-resource estimates for each algorithm, an analysis of the diagonal-synthesis bottleneck that governs near-term hardware execution, and a fully tested, documented, and pip-installable package. QuScope v0.2.0 is available at https://github.com/QuScope/QuScope.

We report a combined scanning tunneling microscopy and atomistic theoretical study of Fe adatoms on the Bi$_2$Te$_3$(111) surface. Topographic imaging at $4.5$~K shows that Fe adatoms in fcc and hcp hollow sites exhibit a threefold-symmetric contrast, consistent with the $C_{3v}$ symmetry of the adsorption site. However, simultaneously acquired differential conductance ($dI/dV$) maps reveal a pronounced reduction in symmetry, evidenced by differential contrast observed at nearest-neighbor Te sites. Density functional theory calculations show that the Fe/Bi$_2$Te$_3$ system undergoes a static Jahn–Teller distortion, reducing the adsorption symmetry from $C_{3v}$ to $C_{1v}$, with the distorted configuration favored by $72.5$~meV. Orbital-projected density of states calculations show that the occupied states near the Fermi level are dominated by $d_{xz}$ and $d_{yz}$ orbitals, whereas the unoccupied states are primarily of $d_{z^2}$, $d_{x^2-y^2}$, and $d_{xy}$ character. The local density of states from these orbitals is in good qualitative agreement with experimental $dI/dV$ spectra. Furthermore, simulated local-density-of-states maps using a tight-binding Green's function approach are consistent with experimental $dI/dV$ maps, confirming that the reduced symmetry originates from the $C_{1v}$ structural distortion.

Gauge invariance is central to modern physics and underpins quantum simulations of lattice gauge theories (LGTs). Existing quantum simulation approaches employ Gauss's law either to energetically suppress gauge-violating processes in analog platforms or to detect and discard gauge-violating outcomes in digital devices. Here we introduce a third paradigm, in which Gauss's law is used to dynamically generate the gauge theory itself from a substantially simpler Hamiltonian. Starting from a readily programmable three-body XXX model, we employ experimentally efficient single-qubit U(1) gauge symmetry-generator terms that induce the dynamics of a U(1) LGT. We implement this approach using 101 qubits on a 156-qubit IBM quantum processor and observe real-time dynamics in quantitative agreement with the target LGT while reducing the entangling-gate depth per Trotter step by a factor of five compared with a direct implementation. Our results establish gauge protection as a resource for Hamiltonian engineering rather than merely symmetry preservation, opening a scalable resource-efficient route towards digital quantum simulations of increasingly complex gauge theories in higher spatial dimensions.

Understanding how a parent insulating state shapes the superconductivity that emerges upon doping is a long-standing problem dating back to Anderson's resonating-valence-bond proposal. The triangular-lattice Hofstadter-Hubbard model with $\pi/2$ flux per plaquette offers an ideal setting: at half filling it hosts two distinct parent states—an integer quantum Hall insulator and a chiral spin liquid—separated by a topological phase transition. Using neural quantum states on tori of up to $432$ sites, we present strong evidence that the transition is continuous, with a vanishing $2e$ charge gap and critical charge fluctuations. Upon doping, we find a topological superconductor on either side of the transition. While the pairing order parameter remains nearly unchanged across the transition, the superfluid stiffness is strongly enhanced near the critical point. The energy scale of the superconductor is therefore set not by which parent state is doped, but by proximity to the transition between them. Our results establish neural quantum states as a powerful tool for understanding the interplay between unconventional electronic correlations and superconductivity.

Spectral transitions in non-Hermitian lattices often arise from the competition between non-reciprocal skin accumulation and inter-component hybridization. In short-range systems formed by two coupled chains, this competition conventionally leads to the logarithmic critical-length law $N_c\sim\ln D$, where $D$ is the transverse separation between the chains. Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws. When only the hybridization couplings are power-law decaying with exponent $\alpha$, the onset becomes algebraic, $N_c\sim D^{\alpha/3}$. When the hoppings within each chain are themselves also power-law decaying, in addition to the hybridization couplings, the system enters a scale-covariant regime for $\alpha<2$, in which the criticality threshold equation depends only on the system aspect ratio $N_c/D$. At $\alpha=2$ and beyond, this regime is followed by a marginal logarithmically corrected and algebraically corrected regimes, respectively. We identify two new non-local mechanisms that enable this unconventional critical hierarchy: a nonanalytic band-edge dispersion from long-range intra-chain hoppings, and parity-mixing hybridization induced by non-reciprocity. Our results show that nonlocality systematically removes the physical length scales i.e. skin depth underlying conventional critical non-Hermitian skin behavior, offering a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.

The eigenstate thermalization hypothesis (ETH) provides the prevailing framework for understanding quantum thermalization and ergodicity in isolated many-body systems. Yet, no general theory describes the continuous onset of ETH violation between the conventional ETH and its complete breakdown. Here, we introduce a two-parameter ansatz for the ETH violation that unifies and distinguishes two mechanisms: fading ergodicity and trapped ergodicity. While fading ergodicity captures the established route to ergodicity breaking, trapped ergodicity describes a distinct scenario in which ETH is violated in finite systems but restored in the thermodynamic limit. We test this framework in the spin-1/2 $J_1$-$J_2$ chains with on-site disorder and linear potential. In both cases, we find that the observed ETH violation is consistent with trapped ergodicity.

We study the six-vertex model on the Sierpinski gasket, a four-coordinated hierarchical fractal with Hausdorff dimension $d_f=\log_23$. Given the importance of dimensionality for the long-wavelength behavior of such models, we specifically consider correlations and confinement as a function of the vertex weights, with the equal-weight point corresponding to the ice model. We calculate the partition function and correlators recursively to obtain a rich phase diagram hosting many different regimes. While the ice model shows entropic charge confinement, a particular four-vertex limit exhibits fractal deconfinement, with the string joining the deconfined charges itself a statistical fractal with fractal dimension $d_l=\log_2(5/2)\approx 1.3$. Finally, we propose a setup as an artificial spin ice to enable experimental study of the rich phenomenology of Sierpinski ice and its generalisations.

Equipped with the recently recognized symmetry structure of mixed states of matter and "strong-weak spontaneous symmetry breaking" (SW-SSB), we develop a quantum particle-vortex duality of emergent model-F and model-A hydrodynamics of 2d boson/rotor systems. This duality relation demonstrates that classical hydrodynamics of 2d bosons can be described in terms of the charge symmetry $U(1)_c$, but also equivalently in terms of the dual (emergent) 1-form symmetry $U(1)^{(1)}_e$, as well as $U(1)_v$ associated with the conservation of vortices. This duality provides a bridge between the hydrodynamics of matter and magnetohydrodynamics.

We present a fermionic lattice Hamiltonian that exactly realizes the $\mathrm{U(1)}_\mathrm{L}\times \mathrm{U(1)}_\mathrm{R}$ global symmetry and the associated chiral anomalies of a massless Dirac fermion in 1+1 dimensions. The construction couples Villain bosons to a Kitaev chain of Majorana fermions, where the bosonic fields are essential for evading Nielsen-Ninomiya-type no-go theorems. For two copies of our model, we realize the anomaly-free $\mathrm{U(1)}_{3450}$ global symmetry and construct symmetric boundary conditions. We analytically demonstrate symmetric mass generation by mapping the symmetry-preserving six-fermion interactions to fermion bilinear terms using fermionic T-duality. Finally, by gauging general anomaly-free global symmetries, we obtain a broad class of lattice chiral gauge theories. As nontrivial applications, we compute the mass spectra of the lattice Schwinger model and the 3450 gauge theory, finding agreement with the corresponding continuum results.

Recent experiments in moiré materials have enabled the realization of a variety of exotic quantum phases. In this context, the Hofstadter-Hubbard model has been proposed as a possible setting for hosting chiral spin liquid. Concurrently, significant progress has been recently made in the computational methods for two-dimensional many-body fermion systems, which makes numerically studying this challenging model a real possibility in genuine 2D geometry. Motivated by these advances, we investigate the putative chiral spin liquid phase in the triangular-lattice Hofstadter-Hubbard model using variational Monte Carlo with neural quantum states (NQS) and projected entangled pair states (PEPS). We observe spin-charge separation directly in real space through numerical spin-pumping simulation and real-time spin and charge motion. In addition, in the context of anyonic superconductivity conjectured in this model, we find a positive two-electron binding energy on small systems, but it decreases below our numerical resolution as the system size increases. Our work demonstrates NQS and PEPS as powerful tools, capable of cross-checking each other, for diagnosing topological order and fractionalized excitations in strongly correlated electronic systems.

Tensor network methods provide powerful analytical and numerical tools for characterizing quantum phases of matter. While the mathematical structure of matrix product states (MPS) is well understood through the MPS fundamental theorem, an analogous understanding for mixed-state tensor networks remains largely absent: if two purification tensors generate the same density matrix, how are they related? In this work, we initiate the study of a fundamental theorem for matrix product locally purifiable density operators (LPDOs) and focus on sequentially generated LPDOs (sLPDOs), a broad subclass admitting an interpretation in terms of successive applications of quantum channels on an initial state. We prove that, under suitable invertibility or cyclic conditions, two sLPDO representations generate the same density matrix for arbitrary system sizes if and only if they are related by a matrix product isometry acting on the purification bonds. Beyond the sLPDO setting, we provide a counterexample that suggests an obstruction to a general fundamental theorem for LPDOs with periodic boundary conditions. Finally, we discuss implications for mixed-state symmetry-protected topological phases, including the possibility of nontrivial phases protected only by weak symmetry conditions.

We construct an exactly solvable Hamiltonian lattice model realizing a 1+1d Dirac fermion, with exact microscopic vector and axial vector $U(1)$ symmetries. The mixed anomaly between these is accommodated by the not-on-site action of the symmetries. Our Hilbert space is a $Z_2$-graded tensor product of local $Z_2$-graded Hilbert spaces which include infinite dimensional rotor degrees of freedom. The Hamiltonian becomes manifestly exactly solvable after a locality-preserving unitary mapping to an equivalent fermionic Villain Hilbert space. Our construction also allows an exactly solvable realization of interacting fermionic Luttinger liquids. At the free Dirac fixed point, our Hamiltonian contains irrelevant interactions, which we compute to leading order.