Quantum Monte Carlo Research Articles

Entanglement Entropy and Deconfined Criticality: Emergent SO(5) Symmetry and Proper Lattice Bipartition.

We study the Rényi entanglement entropy (EE) of the two-dimensional J-Q model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum MonteCarlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-N conformal field theory with SO(N=5) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for cornerless bipartitions. We here use a 45° tilted cut on the square lattice. Beyond supporting an SO(5) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.

Enhanced Pair-Density-Wave Vertices in a Bilayer Hubbard Model at Half Filling.

Motivated by the pair-density-wave (PDW) state found in the one-dimensional Kondo-Heisenberg chain, we report on a determinant quantum MonteCarlo study of pair fields for a two-dimensional half-filled Hubbard layer coupled to an itinerant, noninteracting layer with one electron per site. In a specific range of interlayer hopping, the pairing vertex associated with PDW order becomes more attractive than that for uniform d-wave pairing, although both remain subdominant to the leading antiferromagnetic correlations at half filling. Our result sheds light on where one potentially may find a PDW state in such a model.

Pseudogap Effects in the Strongly Correlated Regime of the Two-Dimensional Fermi Gas.

The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum MonteCarlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.

Quenching of the quantum p-strength in light exotic nuclei

One-nucleon spectroscopic overlaps, their strength or spectroscopic factors (SFs), and nucleon removal cross sections for light nuclei in the mass range A≤12 were evaluated using the fully correlated Quantum Monte Carlo (QMC) wave functions (WFs). Harder (AV18+UX) and softer (NV2+3) bare interactions were used providing consistent results. The SFs were also taken from simple Shell Model (SM) calculations. This structure information was incorporated in the standard three-body Faddeev/Alt-Grassberger-Sandhas reaction formalism to evaluate the (p,pN) cross sections. The results further our understanding of the quenching of the quantum p-shell strength obtained from structure and reactions. We have found the ratios of the total QMC sums of SFs to the SM ones to be uniform and ∼ 3/4. The corresponding ratios of the sums Below Particle Threshold (BPT) of SFs, as well as of total cross sections, deviate strikingly from the uniform trend in some special cases. We find these ratios to be close to unit for Li9→8Li+n and C9→8B+p. In contrast, they are strongly reduced for C11→10C+n and B11→10Be+p mirror transitions, resulting from the quenching of the strength for low-lying 2+ final state transitions. The QMC theoretical cross section BPT for C11(p,pn) is about two times smaller than the experimental data.

Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder.

Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum MonteCarlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.

Helical Luttinger Liquid on a Space-Time Lattice.

The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results because of the fermion-doubling obstruction: a local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here, we show how to work around this obstruction by discretizing both space and time to obtain a local Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum MonteCarlo simulations that preserve the topological protection of an unpaired Dirac cone.

Drag and Thermal Reduction of Spiked Hypersonic Vehicle in Thermochemical Nonequilibrium

This study utilizes the in-house parallel direct simulation Monte Carlo–quantum dynamics method to model the aerodynamic flowfield of a spiked reentry vehicle within a rarefied high-altitude atmosphere. Investigating the flight of spiked aircraft under various flight conditions and spike sizes and considering both the real gas effect and the rarefied gas effect, the aerodynamic characteristic of the aircraft is evaluated. Performance evaluation for effectiveness in drag reduction and thermal protection is based on drag and the maximum stagnation heat flux coefficient at the vehicle’s shoulder. Findings indicate that, in the rarefied atmosphere, the distinction between the characteristic shock intensities of spiked and unspiked vehicles is not pronounced, which results in a drag reduction of approximately 5%, accompanied by a more than 100% increase in thermal effect on the vehicle’s shoulder, obviously poor in effectiveness. Subsequently, this study examines the spiked vehicle equipped with a lateral jet, and this augmented approach achieves a marked reduction in the intensity of the shock wave impacting the vehicle’s shoulder with a drag reduction exceeding 10% and attenuates the thermal impact by over 50% in comparison to the implementation of spiking alone, thereby demonstrating superior performance in terms of effectiveness.

Liquid-Liquid Transition in a Bose Fluid near Collapse.

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this Letter, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum MonteCarlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter η describing its strength. If η exceeds a characteristic value η_{c}, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for η≲η_{c}, finding-in addition to a liquid-vapor transition-a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As η approaches η_{c}, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for η larger than η_{c} our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories.

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Accurate Quantum Monte Carlo Forces for Machine-Learned Force Fields: Ethanol as a Benchmark.

Quantum Monte Carlo (QMC) is a powerful method to calculate accurate energies and forces for molecular systems. In this work, we demonstrate how we can obtain accurate QMC forces for the fluxional ethanol molecule at room temperature by using either multideterminant Jastrow-Slater wave functions in variational Monte Carlo or just a single determinant in diffusion Monte Carlo. The excellent performance of our protocols is assessed against high-level coupled cluster calculations on a diverse set of representative configurations of the system. Finally, we train machine-learning force fields on the QMC forces and compare them to models trained on coupled cluster reference data, showing that a force field based on the diffusion Monte Carlo forces with a single determinant can faithfully reproduce coupled cluster power spectra in molecular dynamics simulations.

Exact Numerical Solution of the Fully Connected Classical and Quantum Heisenberg Spin Glass.

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time quantum MonteCarlo algorithm. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analog, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

Efficient calculation of unbiased atomic forces in ab initio variational Monte Carlo

quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wave functions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose an efficient method to obtain unbiased atomic forces and pressures in the variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz or the Jastrow antisymmetrized geminal power ansatz, exploiting the gauge-invariant and locality properties of their geminal representation. We demonstrate the effectiveness of our method for H2 and Cl2 molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces. Published by the American Physical Society 2024

Measuring the Boundary Gapless State and Criticality via Disorder Operator.

The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum MonteCarlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)_{1} CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.

Quantum Slush State in Rydberg Atom Arrays.

In this Letter, we propose an exotic quantum state that does not order at zero temperature in a Rydberg atom array with antiblockade mechanism. By performing an unbiased large-scale quantum MonteCarlo simulation, we investigate a minimal model with facilitated excitation in a disorder-free system. At zero temperature, this model exhibits a heterogeneous structure of liquid and glass mixture. This state, dubbed quantum slush state, features a quasi-long-range order with an algebraic decay for its correlation function, and is different from most well-established quantum phases of matter.

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

Enhancing Autonomous Underwater Vehicle Decision Making through Intelligent Task Planning and Behavior Tree Optimization

The expansion of underwater scenarios and missions highlights the crucial need for autonomous underwater vehicles (AUVs) to make informed decisions. Therefore, developing an efficient decision-making framework is vital to enhance productivity in executing complex tasks within tight time constraints. This paper delves into task planning and reconstruction within the AUV control decision system to enable intelligent completion of intricate underwater tasks. Behavior trees (BTs) offer a structured approach to organizing the switching structure of a hybrid dynamical system (HDS), originally introduced in the computer game programming community. In this research, an intelligent search algorithm, MCTS-QPSO (Monte Carlo tree search and quantum particle swarm optimization), is proposed to bolster the AUV’s capacity in planning complex task decision control systems. This algorithm tackles the issue of the time-consuming manual design of control systems by effectively integrating BTs. By assessing a predefined set of subtasks and actions in tandem with the complex task scenario, a reward function is formulated for MCTS to pinpoint the optimal subtree set. The QPSO algorithm is then leveraged for subtree integration, treating it as an optimal path search problem from the root node to the leaf node. This process optimizes the search subtree, thereby enhancing the robustness and security of the control architecture. To expedite search speed and algorithm convergence, this paper recommends reducing the search space by pre-grouping conditions and states within the behavior tree. The efficacy and superiority of the proposed algorithm are validated through security and timeliness evaluations of the BT, along with comparisons with other algorithms for automatic AUV decision control behavior tree design. Ultimately, the effectiveness and superiority of the proposed algorithm are corroborated through simulations on a multi-AUV complex task platform, showcasing its practical applicability and efficiency in real-world underwater scenarios.

Electric Polarization from a Many-Body Neural Network Ansatz.

Abinitio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wave function ansatz combined with quantum MonteCarlo method to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and reestablished its thickness dependence. Overall, this approach provides a powerful tool to accurately describe electron correlation in the modern theory of polarization.

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation.

The "symmetric mass generation" (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum MonteCarlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true (2+1)d unitary conformal field theory.

Stochastic series expansion quantum Monte Carlo for Rydberg arrays

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.

Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation – i.e. simulation of the risk factor evolution over time to generate probability distributions – into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.