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A variety of generative neural networks recently adopted from machine learning have provided promising strategies for studying quantum matter. In particular, the success of autoregressive models in natural language processing has motivated their use as variational ansätze, with the hope that their demonstrated ability to scale will transfer to simulations of quantum many-body systems. In this paper, we introduce an autoregressive framework to calculate finite-temperature properties of a quantum system based on the imaginary-time evolution of an ensemble of pure states. We find that established approaches based on minimally entangled typical thermal states (METTS) have numerical instabilities when an autoregressive recurrent neural network is used as the variational ansätz. We show that these instabilities can be mitigated by evolving the initial ensemble states with a unitary operation, along with applying a threshold to curb runaway evolution of ensemble members. By comparing our algorithm to exact results for the spin 1/2 quantum XY chain, we demonstrate that autoregressive typical thermal states are capable of accurately calculating thermal observables. 

We systematically derive the dissipationless quantum kinetic equation for a multiband free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band diagonalize the dynamics. Expanding to the second order in gradients, which is beyond the semiclassical limit, we give a complete analysis of the band-resolved thermodynamics and transport properties, especially those arising from the quantum geometric tensor. We apply our framework to a Bloch band theory under electric fields near equilibrium and find the linear and nonlinear transport coefficients. We also obtain the dynamical density-density response functions in the metallic case, including quantum metric corrections. Our results and approach can be applied very generally to multiband problems even in situations with spatially varying Hamiltonians and distributions. 

Moiré materials provide exciting platforms for studying the interplay of strong electronic correlation and large magnetic flux effects. We study the lightly doped Hofstadter-Hubbard model on a triangular lattice through the large-scale density matrix renormalization group and determinantal quantum Monte Carlo simulations. We find strong evidence for a robust chiral superconducting (SC) phase with dominant power-law pairing correlations and a quantized spin Chern number. The SC phase emerges at very weak interaction and grows stronger at intermediate interaction strengths ( $U$ ) for a wide range of hole doping. We also discuss the possible distinct nature of the normal state in different $U$ regimes. Our Letter provides theoretical insights into the emergence of topological superconductivity from doping topological Chern bands or magnetic-flux-induced chiral spin liquid states of Moiré materials. 

Motivated by twisted transition metal dichalcogenides (TMDs), we study an extended Hubbard model with both onsite and off-site repulsive interactions, in which Mott insulating states with concomitant charge order occur at fractional fillings. To resolve the charge ordering as well as the fate of the local moments formed thereby, we perform large-scale density matrix renormalization group calculations on cylindrical geometries for several filling fractions and ranges of interaction strength. Depending on the precise parameter regime, both antiferromagnetically ordered as well as quantum-disordered states are found, with a particularly prominent example being a quantum spinliquid type ground state on top of charge ordering with effective kagomé geometry. We discuss the different mechanisms at play in stabilizing various electronic and magnetic states. The results suggest that moiré TMDs are a promising venue for emergent quantum magnetism of strongly interacting electrons. 

We study the gyrotropic magnetic effect (GME), the low-frequency limit of optical gyrotropy, in metals and semimetals coupled to chiral spin textures. In these systems, the chiral spin texture which lacks inversion symmetry can imprint itself upon the electronic structure through Hund s coupling, leading to novel low- frequency optical activity. Using perturbation theory and numerical diagonalization of both relativistic and nonrelativistic models of conduction electrons coupled to spin textures, we analyze how the GME manifests in both single-q and multi-q textures. Analytical expressions for the rotatory power are derived in terms of universal scaling functions. Estimates based on realistic material parameters reveal an experimentally viable range of values for the rotatory power. The GME arises from the orbital and spin magnetic moments of conduction electrons, with the orbital part closely tied to Berry curvature and playing a significant role in relativistic metals but not so in nonrelativistic metals where there is no inherent Berry curvature. The spin contribution to the GME can be significant in nonrelativistic metals with a large Fermi energy. Our Letter shows that the GME can be a sensitive probe of magnetic chirality and symmetry breaking in metallic chiral magnets. 

The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended $t$ - $J$ model where the background spins form a ${\mathbb{Z}}_2$ quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid. 

We study the driven-dissipative Bose-Hubbard model with an all-to-all hopping term in the system Hamiltonian, while subject to incoherent pumping and decay from the environment. This system is naturally probed in several recent experiments on excitons in WS₂/WSe₂moiré systems, as well as quantum simulators. By positing a particular form of coupling to the environment, we derive the Lindblad jump operators and show that, in certain limits, the system admits a closed-form expression for the steady-state density matrix. Away from the exactly solvable regions, the steady state can be obtained numerically for 100s to 1,000s of sites. We study the nonequilibrium phase diagram and phase transitions, which qualitatively matches the equilibrium phase diagram, agreeing with the intuition that increasing the intensity of the light is equivalent to changing the bosonic chemical potential. However, the steady states are far from thermal states, and the nature of the phase transitions is changed. 

We present the theory of the longitudinal spin Seebeck effect between a Heisenberg spin-1/2 chain and a conductor. The effect consists of the generation of a spin current across the spin chain-conductor interface in response to the temperature difference between the two systems. In this setup, the current is given by the convolution of the local spin susceptibilities of the spin chain and the conductor. We find the spin current to be fully controlled, both in the magnitude and the sign, by the backscattering interaction between spinons, fractionalized spin excitations of the Heisenberg chain. In particular, it vanishes when the spinons form a noninteracting spinon gas. Our analytical results for the local spin susceptibility at the open end of the spin chain are in excellent agreement with numerical density matrix renormalization group simulations.