Shiwei Zhang

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parametrized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators that form the backbone of the method can become unstable or biased due to the presence of nodes, a ubiquitous feature of quantum wave functions. In the continuum, this results in heavy-tailed estimators with potentially divergent variances, while in discrete Hilbert spaces the sampling distribution can miss parts of the support needed to form unbiased estimators. These statistical pathologies lead to unreliable optimization trajectories in stochastic reconfiguration or incorrect variational dynamics in time-dependent variational Monte Carlo (t-VMC) and severely limit the power of the numerical simulations. We introduce blurred sampling to address these difficulties. The method has a number of rigorous properties that make it well behaved, effective, and computationally efficient. Additionally, it is a postprocessing approach that can be used without modifying the underlying sampler and incurs only minimal overhead. We demonstrate its effectiveness in a broad range of problems—including ground-state optimization in both continuum and discrete settings as well as in time-dependent variational Monte Carlo, where it resolves previously identified failure modes—and further apply it to large-scale problems in spin dynamics. This work establishes a broadly applicable framework for robust VMC and t-VMC calculations.

Finite-momentum pairing, exemplified by Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states, represents a paradigmatic form of unconventional superfluidity driven by Fermi-surface mismatch, but its detection in two-dimensional systems has remained elusive. Here we study a doped, spin-imbalanced attractive Hubbard model using a combined experimental and computational approach, based on quantum gas microscopy and constrained-path auxiliary-field quantum Monte Carlo, with direct comparisons showing quantitative agreement for short-range correlations at experimentally accessible temperatures. We identify broad regimes in density and magnetization where FFLO correlations emerge, and establish their finite-temperature evolution, with clear signatures of finite-momentum pairing already appearing at experimentally accessible temperatures. Spin–XY correlations are identified as a robust, directly measurable proxy for FFLO physics. Quantitative characterizations are obtained on the temperature dependence of a variety of observables and correlations, which elucidate the interplay of pairing with competing orders.

Electron Wigner solids (WSs)^{1,2,3,4,5,6,7,8,9,10,11,12} provide an ideal system for understanding the competing effects of electron–electron and electron–disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has been limited by a lack of single-defect-resolved experimental measurements as well as accurate theoretical tools to enable realistic experiment/theory comparison. Here we overcome these limitations by combining atomically resolved scanning tunnelling microscopy (STM) with neural-quantum-state quantum Monte Carlo (NQS-QMC) simulation of disordered 2D electron WSs to discover new disorder-induced physical regimes of correlated electron behaviour. STM was used to image the electron density (n_e)-dependent evolution of electron WSs in gate-tunable bilayer MoSe₂ (BL-MoSe₂) devices with varying long-range (n_LR) and short-range (n_SR) disorder densities. These images were compared with NQS-QMC simulations using realistic disorder maps extracted from experiment, thus allowing the roles of different disorder types to be disentangled. We identify two distinct physical regimes for disordered electron WSs that depend on n_SR. For n_SR ≲ n_e, the WS behaviour is dominated by long-range disorder and features extensive mixed solid–liquid phases, a new type of local re-entrant melting/crystallization and prominent Friedel oscillations. By contrast, when n_SR ≫ n_e, these features are suppressed and a more robust amorphous WS phase emerges that persists to higher n_e, highlighting the importance of short-range disorder in this regime. Our work establishes a powerful framework for studying disordered quantum solids through a combined experimental–theoretical approach.

Moiré systems have emerged as an exciting new tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of ν _m = 1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form singlet-like valence bond states which restore local C ₆ symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems and opportunities to engineer exotic properties in a system within current experimental setups. This discovery signals a new level of predictive power in quantum many-body computations enabled by neural networks and machine learning.

We systematically investigate the calculation of excited states in quantum chemistry using auxiliary field quantum Monte Carlo (AFQMC). Symmetry allows targeting of the lowest triplet excited states in AFQMC based on restricted open-shell determinants, effectively as a ground-state calculation. For open-shell singlet states, excited-state calculations can be stabilized with the appropriate trial states, but their quality can have a larger effect on the accuracy in AFQMC. We find that active space-based configuration interaction trial states are often not sufficient to obtain accurate results. We instead use truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states. We benchmark the performance of these calculations on a set of small and medium molecules and polyacenes, focusing on predominantly single excitations. We find that the AFQMC results, obtained at a per-sample cost scaling of O(N6), are systematically more accurate than those obtained using EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets. In regimes where EOM-CC triples are impractical, these results position AFQMC as a scalable, higher-accuracy complement for low-lying excited states.

We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as determinantal quantum Monte Carlo (DQMC), are applied in many situations and differ in details, but they share a foundation in field theory, and often involve fermion determinants whose symmetry properties make the algorithm sign-problem-free. We show that the infinite variance problem arises as the observables computed in DQMC tend to form heavy-tailed distributions. To remedy this issue retrospectively, we introduce a tail-aware error estimation method to correct the otherwise unreliable estimates of confidence intervals. Furthermore, we demonstrate how to perform DQMC calculations that eliminate the infinite variance problem for a broad class of observables. Our approach is an exact bridge link method, which involves a simple and efficient modification to the standard DQMC algorithm. The method introduces no systematic bias and is straightforward to implement with minimal computational overhead. Our results establish a practical and robust solution to the infinite variance problem, with broad implications for improving the reliability of a variety of fundamental fermion simulations.

We introduce an efficient approach to implement correlated many-body trial wave functions in auxiliary-field quantum Monte Carlo (AFQMC). To control the sign/phase problem in AFQMC, a constraint is derived from an exact gauge condition but is typically imposed approximately through a trial wave function or trial density matrix, whose quality can affect the accuracy of the method. Furthermore, the trial wave function can also affect the efficiency through importance sampling. The most natural form of the trial wave function has been single Slater determinants or their linear combinations. More sophisticated forms, for example, with the inclusion of a Jastrow factor or other explicit correlations, have been challenging to use, and their implementation is often assumed to require a quantum computer. In this work, we demonstrate that a large class of correlated wave functions, written in the general form of multi-dimensional integrals over hidden or auxiliary variables times Slater determinants, can be implemented as a trial wave function by coupling the random walkers to a generalized Metropolis sampling. We discuss the fidelity of AFQMC with stochastically sampled trial wave functions, which are relevant to both quantum and classical algorithms. We illustrate the method and show that an efficient implementation can be achieved, which preserves the computational scaling of AFQMC. We test our method in molecules under bond stretching and in transition metal diatomics. Significant improvements are seen in both accuracy and efficiency over typical trial wave functions, and the method yields total ground-state energies systematically within chemical accuracy. The method can be useful for incorporating other advanced wave functions, for example, neural quantum state wave functions optimized from machine learning techniques, or for other forms of fermion quantum Monte Carlo.

In devices based on two-dimensional electron gases (2DEGs), gate electrodes can be used to tune the electronic properties by controlling the electron density. Despite the prevalence of such gated systems, the properties of 2DEGs in these environments remain poorly understood quantitatively. To address this, we have studied the 2DEG in a dual-gate geometry using quantum Monte Carlo simulations alongside simpler approximate methods, and we have mapped out the phase diagram of the gated 2DEG as a function of electron density and gate distance. We find that the Wigner crystal is unstable at all densities when the gates are sufficiently close to the 2DEG, and we identify the critical gate distance at which the Wigner crystal phase appears. For larger gate separations, we determine the phase boundary for the reentrant crystal to liquid transition that occurs with decreasing density. Our Letter is particularly relevant to Wigner crystal phases recently observed in a variety of gated two-dimensional materials.