We employ real-space variational quantum Monte Carlo methods with resonating valence bond many-body wave functions to investigate electron correlation effects in the kagome system ${\text{Zn}}_x{\text{Cu}}_{4-x}{\text{O}}_6$. Using three trial wave functions of the Slater-Jastrow type, where (i) only the Jastrow correlation factor is optimized and the orbitals obtained by density functional theory, (ii) both the Jastrow factor and the Slater determinant are optimized, and (iii) additionally the Slater determinant is substituted by an antisymmetrized-geminal power-wave function, we analyze static and dynamic correlation energies across concentrations $x=0,\frac{1}{3},\frac{2}{3},1$. Optimizing the Slater determinant significantly enhances the correlation energy by approximately $\sim -73\left(4\right)\text{mHa}$ per electron. Eventually, the emergence of a quantum spin liquid state driven by a long-range correlation energy is discussed.

Excitons, namely, neutral excitations in a system of electrons arising from the electron-hole interaction, are often essential to explain optical measurements in materials. They are governed by the Bethe-Salpeter equation, which can be cast into a matrix form that is formally analogous to the one for electrons at the mean-field level. However, constructing the corresponding excitonic Hamiltonian in practice is challenging, specially from a computational perspective if one wishes to surpass effective models. Methods that enable such calculations from the different density-functional theory frameworks currently available are, therefore, convenient. In this work, we present an approach to solve the BSE starting from a self-consistent calculation in any nonmetallic solid by evaluating the electron-hole kernel in real space with a localized, Gaussian-type basis. It is based on the Gaussian density fitting or resolution of the identity approximation to reduce the initial quartic scaling in the basis dimension, in combination with the use of Ewald-type potential functions to automatically sum the conditionally convergent lattice series. The method inherits the features of the localized basis, in particular the reduced computational requirements due to the small and tunable Hilbert-space dimension, the natural adaptation to lower-dimensional systems or the possibility to evaluate optical matrix elements exactly. As an illustration of the computational implementation, we provide examples of exciton spectra and optical absorption in some paradigmatic 2D and 3D materials where the single-particle approximation fails qualitatively.

We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of $1/3,1/2$, and $2/3$ to model the dynamics of generalized Wigner crystals in moiré heterostructures. At low temperatures where thermal fluctuations are irrelevant, for commensurate fillings we find a strongly pinned state that depins into a sliding crystal, while at incommensurate fillings the depinning threshold is strongly reduced. For fillings below $1/2$, the depinning occurs in a two-step process. Above the first depinning threshold, there is an extended range of drives where the conduction occurs via the sliding of antikinks along the charge stripes, followed by a second threshold where all the charges begin to slide. At finite temperatures, the external driving reduces the effective melting temperature at commensurate fillings and enhances creep at incommensurate fillings. We show that depinning into different sliding states, such as moving fluids or moving crystals, produces nonlinear features in the transport curves. We also show that transport is asymmetric on either side of a commensurate filling due to the different dynamics for interstitials versus holes in the commensurate structure. A variety of sliding states should be accessible for generalized Wigner crystals at finite temperatures even for low drives. If experiments can realize sliding dynamics in moiré systems, it would open another class of commensurate and incommensurate phases for study. Additionally, the sliding dynamics and antikink flow could provide unique functionalities for charge transport in moiré heterostructures.

We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semiclassical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a Möbius graph evolves with increased annealing parameters. Our findings indicate that these semiclassical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the manifold reduction method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian's energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from combining classical and quantum annealing techniques.

Neural quantum states (NQSs) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly correlated electrons using this ansatz.

Two-dimensional Mott insulators host antiferromagnetic (AFM) correlations that are predicted to enhance the attractive interaction between empty (holons) and doubly occupied (doublons) sites, creating a novel pathway for exciton formation. However, experimental confirmation of this spin-mediated binding mechanism remains elusive. Leveraging the distinct magnetic critical properties of the Mott antiferromagnets ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, we show using time-resolved THz spectroscopy that excitons exist only at temperatures below where short-range AFM correlation develops. The excitons remain stable up to photodoping densities approaching the predicted excitonic Mott insulator-to-metal transition, revealing a unique robustness against screening. Our results establish the viability of spin-bound excitons and introduce opportunities for excitonic control through magnetic degrees of freedom.

We investigate the electrical transport properties of the minivalley polarized state proposed recently in slightly doped Bernal bilayer graphene (BLG) in large electric displacement fields. By minimizing the Hartree-Fock (HF) energy functional, we first confirm the appearance of minivalley polarized phase. At the low carrier doping regime, the one-pocket state will be stabilized where only one of the trigonal-wrapping-induced Fermi pockets near the atomic-valley center is filled. Then we study the electrical transport of the one-pocket state by solving the Boltzmann equation. We find that the valley polarization could be easily flopped by an in-plane electrical field, which will lead to hysteresis loop in the direct current (DC) $I\text{−}V$ curves. Such irreversible current responses in the DC limit will directly induce strong nonlinear and nonreciprocal alternating current (AC) responses, which has been already observed in the recent experiments on BLG.

Magic-angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings or smaller lattice sizes. We employ a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers intervalley-coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.

We investigate the prospect of using ultracold alkali diatomic molecules to implement many-body quantum systems with $\mathrm{SU}\left(N\right)$ symmetry. Experimentally accessible molecules offer large $N$ for both bosonic and fermionic systems, with both attractive and repulsive interactions. We carry out coupled-channel scattering calculations on pairs of NaK, NaRb, and NaCs molecules that are shielded from destructive collisions with static electric fields. We develop new methods to handle the very large basis sets required to include nuclear spins. We show that all the molecules studied have the properties required for $\mathrm{SU}\left(N\right)$ symmetry: the collisions are principally elastic, and the scattering lengths depend only weakly on the spin states of the molecules. The rates of spin-changing inelastic collisions are very low. We develop and test a semiclassical model of the spin dependence and find that it performs well.

We introduce two disorder-free variants of the Sachdev-Ye-Kitaev (SYK) model, demonstrate their integrability, and study their static and dynamical properties. Unlike diagrammatic techniques, the integrability of these models allows us to obtain dynamical correlation functions even when the number of Majorana fermions is finite. From the solutions, we find that out-of-time-order correlators (OTOCs) in these models exhibit exponential growth at early times, resembling that of many-body quantum chaotic systems, such as those with disorder or external kick terms, despite their large $N$ behavior differing from that of typical chaotic systems. Conversely, our analysis shows no evidence of random-matrix behavior in level spacing statistics or the spectral form factor. Our findings illustrate that the clean versions of the SYK models represent simple but nontrivial examples of disorder-free quantum many-body systems displaying chaoslike behavior of OTOCs.

Geometric effects in curvilinear nanomagnets can enable chiral, anisotropic, and even magnetoelectric responses. Here, we study the effects of magnetic frustration in curvilinear (quasi-)one-dimensional magnets represented by spin chains arranged along closed space curves of constant torsion. Considering the cases of easy- and hard-axis anisotropy in ferro- and antiferromagnetic samples, we determine their ground states and analyze the related magnetoelectric multipoles. A constant torsion along the chain results in alternating regions of high and low curvature, facilitating the spin spiral state perturbed by the (anti)periodic boundary conditions on the magnetic order parameter. While easy-axis ferromagnetic chains develop a purely toroidal configuration with the magnetic toroidal moment oriented along the geometry symmetry axis, hard-axis antiferromagnetic chains support multiple magnetic toroidal domains. Our findings suggest that tailoring curvature and torsion of a spin chain enables a different physical mechanism for magnetic frustration, which can be observed in the inhomogeneity of the magnetic order parameter and in the local ferrotoroidal responses.

Electron hydrodynamics refers to the transport regime where electrons collectively behave like a fluid. Its realization requires pure materials, some of which, such as bilayer graphene or ${\mathrm{PdCoO}}_2$, are anisotropic so that different in-plane transport directions can be defined. Collective electron flow also benefits from geometrically engineered devices because it is highly dependent on the nonuniformity of the electron flow. Here we analyze carrier transport in anisotropic materials where remarkable effects emerge after the proper directional design of the device. Simulations based on the Boltzmann transport equation demonstrate that electrical properties are clearly different when the device is set in the easy or the hard transport directions, namely, when the transport channel is aligned or not aligned to the group velocity at the Fermi level, respectively. Most importantly, the standard signatures of viscous electron flow, such as Poiseuille flow, superballistic conduction, and the formation of whirlpools, are enhanced when the anisotropic device operates in the hard transport directions. As a result, we demonstrate that electron hydrodynamics leads to a different route for efficient charge transport in the hard in-plane transport directions.

Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior of the strongly entangled systems. We straightforwardly employ the simple dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. Despite the simplicity of the method, the effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are demonstrated, even when the time evolution at long time exhibits complicated features such as a volume-law entanglement entropy and consequential power-law decays of correlations characteristic of systems with long-ranged quantum entanglements unlike fluid dynamics. The present method, though simple, enables accurate forecasts amazingly at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percentages of noise do not affect the prediction accuracy destructively.

With the realization of controlled quantum systems, exploring excitations beyond the resonant case opens new possibilities. We investigate an extended Jaynes-Cummings model in which two nondegenerate photon modes are coupled off resonantly to a quantum emitter. This allows us to identify few-photon scattering mechanisms that lead to a full inversion of the emitter while transferring off-resonant photons from one mode to another. This behavior is connected to recent measurements of a two-level emitter scattering two off-resonant photons simultaneously. Furthermore, our results can be understood as a quantized analog of the recently developed off-resonant quantum control scheme known as swing-up of quantum emitter (SUPER). Our intuitive formalism gives deeper insight into the interaction of a two-level emitter with off-resonant light modes with the prospect of novel photonic applications.