Quantum Monte Carlo Simulations Research Articles

Learning quantum phase transitions through topological data analysis

We implement a computational pipeline based on a recent machine learning technique, namely the Topological Data Analysis (TDA), that has the capability of extracting powerful information-carrying topological features. We apply such a method to the study quantum phase transitions and, to showcase its validity and potential, we exploit such a method for the investigation of two paramount important quantum systems: the 2D periodic Anderson model and the Hubbard model on the honeycomb lattice, both cases on the half-filling. To this end, we have performed unbiased auxiliary field quantum Monte Carlo simulations, feeding the TDA with snapshots of the Hubbard-Stratonovich fields through the course of the simulations The quantum critical points obtained from TDA agree quantitatively well with the existing literature, therefore suggesting that this technique could be used to investigate quantum systems where the analysis of the phase transitions is still a challenge.

Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions.

The competition between kinetic energy and Coulomb interactions in electronic systems leads to complex many-body ground states with competing orders. Here we present zinc oxide-based two-dimensional electron systems as a high-mobility system to study the low-temperature phases of strongly interacting electrons. An analysis of the electronic transport provides evidence for competing correlated metallic and insulating states with varying degrees of spin polarization. Some features bear quantitative resemblance to quantum Monte Carlo simulation results, including the transition point from the paramagnetic Fermi liquid to Wigner crystal and the absence of a Stoner transition. At very low temperatures, we resolve a non-monotonic spin polarizability of electrons across the phase transition, pointing towards a low spin phase of electrons, and a two-order-of-magnitude positive magnetoresistance that is challenging to understand within traditional metallic transport paradigms. This work establishes zinc oxide as a platform for studying strongly correlated electrons in two dimensions.

Projection of infinite- U Hubbard model and algebraic sign structure

We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-$U$ Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure -- a power law dependence of average sign on system size. We demonstrate our scheme on the infinite-$U$ $SU(2N)$ fermionic Hubbard model on both a square and honeycomb lattice at half-filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or two-dimensional Moir\'e systems; among one of them at certain non-half-integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that $SU(2N)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.

Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum MonteCarlo Study.

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum MonteCarlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

A pathway toward high-throughput quantum Monte Carlo simulations for alloys: A case study of two-dimensional (2D) GaSxSe1-x.

The study of alloys using computational methods has been a difficult task due to the usually unknown stoichiometry and local atomic ordering of the different structures experimentally. In order to combat this, first-principles methods have been coupled with statistical methods such as the cluster expansion formalism in order to construct the energy hull diagram, which helps to determine if an alloyed structure can exist in nature. Traditionally, density functional theory (DFT) has been used in such workflows. In this paper, we propose to use chemically accurate many-body variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods to construct the energy hull diagram of an alloy system due to the fact that such methods have a weakerdependence on the starting wavefunction and density functional, scale similarly to DFT with the number of electrons, and have had demonstrated success for a variety of materials. To carry out these simulations in a high-throughput manner, we propose a method called Jastrow sharing, which involves recycling the optimized Jastrow parameters between alloys with different stoichiometries. We show that this eliminates the need for extra VMC Jastrow optimization calculations and results in significant computational cost savings (on average 1/4 savings of total computational time). Since it is a novel post-transition metal chalcogenide alloy series that has been synthesized in its few-layer form, we used monolayer GaSxSe1-x as a case study for our workflow. By extensively testing our Jastrow sharing procedure for monolayer GaSxSe1-x and quantifying the cost savings, we demonstrate how a pathway toward chemically accurate high-throughput simulations of alloys can be achieved using many-body VMC and DMC methods.

Prospects for single-photon sideband cooling of optically trapped neutral atoms

We propose a novel cooling scheme for realising single photon sideband cooling on particles trapped in a state-dependent optical potential. We develop a master rate equation from an ab-initio model and find that in experimentally feasible conditions it is possible to drastically reduce the average occupation number of the vibrational levels by applying a frequency sweep on the cooling laser that sequentially cools all the motional states. Notably, this cooling scheme works also when a particle experiences a deeper trap in its internal ground state than in its excited state, a condition for which conventional single photon sideband cooling does not work. In our analysis, we consider two cases: a two-level particle confined in an optical tweezer and Li atoms confined in an optical lattice, and find conditions for efficient cooling in both cases. The results from the model are confirmed by a full quantum Monte Carlo simulation of the system Hamiltonian. Our findings provide an alternative cooling scheme that can be applied in principle to any particle, e.g. atoms, molecules or ions, confined in a state-dependent optical potential.

Morphology of dipolar Bose droplets

The ground state of a free standing, self-bound droplet comprising four hundred dipolar Bose particles with aligned dipole moments, with an additional purely repulsive two-body interaction, is investigated by Quantum Monte Carlo simulations. The focus here is on the evolution of the cluster as the effective range of the repulsive interaction is varied. We identify a “classical” regime, in which binding arises exclusively from the dipolar potential energy and the cluster is a quasi-one-dimensional filament, and a “quantum” regime of prolate droplets, held together to a significant degree by quantum-mechanical exchanges. The transition between the two regimes occurs abruptly.

Embedding Overhead Scaling of Optimization Problems in Quantum Annealing

In order to treat all-to-all connected quadratic binary optimization problems (QUBO) with hardware quantum annealers, an embedding of the original problem is required due to the sparsity of the hardware's topology. Embedding fully-connected graphs - typically found in industrial applications - incurs a quadratic space overhead and thus a significant overhead in the time to solution. Here we investigate this embedding penalty of established planar embedding schemes such as minor embedding on a square lattice, minor embedding on a Chimera graph, and the Lechner-Hauke-Zoller scheme using simulated quantum annealing on classical hardware. Large-scale quantum Monte Carlo simulation suggest a polynomial time-to-solution overhead. Our results demonstrate that standard analog quantum annealing hardware is at a disadvantage in comparison to classical digital annealers, as well as gate-model quantum annealers and could also serve as benchmark for improvements of the standard quantum annealing protocol.

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar–Bernevig–Hughes model

We study the higher-order topological spin phases based on a spin analogue of Benalcazar–Bernevig–Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

Inexorable edge Kondo breakdown in topological Kondo insulators

Kondo breakdown is one of the most intriguing problems in strongly correlated electron systems, as it is rooted in many anomalous electron behaviors found in heavy-fermion materials. In Kondo lattice systems, Kondo breakdown can arise from either strong magnetic frustrations or critical fluctuations of collective modes. Here, we reveal another type of Kondo breakdown with a fully different origin in interacting topological Kondo insulators. By employing numerically exact quantum Monte Carlo simulations, we show that with open boundary conditions, Kondo screening is inexorably destroyed by interaction effects on edges or corners in these systems. We argue that the Kondo breakdown is enforced by the symmetries of the system, because the ground states are symmetry-protected Haldane phases.

Hierarchical single-ion anisotropies in spin-1 Heisenberg antiferromagnets on the honeycomb lattice

We examine the thermal properties of the spin-1 Heisenberg antiferromagnet on the honeycomb lattice in the presence of an easy-plane single-ion anisotropy as well as the effects of an additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze the scaling of the correlation length near the thermal phase transition into the ordered phase. This allows us to quantify the temperature regime above the critical point in which -- in spite of the additional in-plane easy-axis anisotropy -- characteristic easy-plane physics, such as near a Berezinskii-Kosterlitz-Thouless transition, can still be accessed. Our theoretical analysis is motivated by recent neutron scattering studies of the spin-1 compound BaNi${}_2$V${}_2$O${}_8$ in particular, and it addresses basic quantum spin models for generic spin-1 systems with weak anisotropies, which we probe over the full range of experimentally relevant correlation length scales.

Zooming in on heavy fermions in Kondo lattice models

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as $e^{-W/J_k}$ with $W$ the bandwidth and $J_k$ the Kondo coupling, the residue of the composite fermion tracks $J_k$. This result holds down to $J_k/W = 0.05$, and confirms the point of view that magnetic ordering, present below $J_k/W = 0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for SU($N$) generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large $J_k$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.

Higher-order topological Mott insulator on the pyrochlore lattice

We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a {mathbb {Z}}_{4} spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.

Topological terms on topological defects: A quantum Monte Carlo study

Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\theta$-term implies that a domain wall of the Z$_2$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a $1+1$ dimensional SO(3) non-linear sigma model with $\theta$-term at $\theta = \pi$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the Z$_2$ topological defect. This concept can be generalized to higher dimensions where $2+1$ dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.

Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions

The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices.

Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin‐resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi‐Tosi‐Land‐Sjölander scheme with the QMC data to remove finite‐size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)] and configuration path integral Monte Carlo/permutation‐blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117, 115701 (2016)].

Quantum Monte Carlo study of honeycomb antiferromagnets under a triaxial strain

The honeycomb antiferromagnet under a triaxial strain is studied using the quantum Monte Carlo simulation. The strain dimerizes the exchange couplings near the corners, thus destructs the antiferromagnetic order therein. The antiferromagnetic region is continuously reduced by the strain. For the same strain strength, the exact numerical results give a much smaller antiferromagnetic region than the linear spin-wave theory. We then study the strained $XY$ antiferromagnet, where the magnon pseudo-magnetic field behaves quite differently. The $0$th Landau level appears in the middle of the spectrum, and the quantized energies above (below) it are proportional to $n^{\frac{1}{3}} (n^{\frac{2}{3}})$, which is in great contrast to the equally-spaced ones in the Heisenberg case. Besides, we find the antiferromagnetic order of the $XY$ model is much more robust to the dimerization than the Heisenberg one. The local susceptibility of the Heisenberg case is extracted by the numerical analytical continuation, and no sign of the pseudo-Landau levels is resolved. It is still not sure whether the result is due to the intrinsic problem of the numerical analytical continuation. Thus the existence of the magnon pseudo-Landau levels in the spin-$\frac{1}{2}$ strained Heisenberg Hamiltonian remains an open question. Our results are closely related to the two-dimensional van der Waals quantum antiferromagnets and may be realized experimentally.

Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a {{mathbb{Z}}}_{2} quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

Non-Hermitian Hubbard model without the sign problem

We study the Hubbard model with non-Hermitian asymmetric hopping terms. The conjugate hopping terms are introduced for two spin components so that the negative sign is canceled out. This ensures that the quantum Monte Carlo simulation is free from the negative sign problem. We analyze the antiferromagnetic order and its suppression by the non-Hermiticity.

Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudo-density matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudo-snapshots of occupation numbers on large systems can be produced. There is a sign problem even when the conventional determinantal QMC algorithm can be made sign-problem free, and every pseudo-snapshot comes with a sign and a reweighting factor. Nonetheless, this "sampling sign problem" turns out to be weak and manageable in a large, relevant parameter regime. The method allows to compute distribution functions of arbitrary quantities defined in occupation number space and, from a practical point of view, facilitates the computation of complicated conditional correlation functions. While the projective measurements in quantum gas microscope experiments achieve direct sampling of occupation number states from the density matrix, the presented numerical method requires a Markov chain as an intermediate step and thus achieves only indirect sampling, but the full distribution of pseudo-snapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements