Quantum Monte Carlo Simulations Research Articles

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.

Semigroup approach to the sign problem in quantum Monte Carlo simulations

Semigroup approach to the sign problem in quantum Monte Carlo simulations

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.

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

We study the ferromagnetic transverse-field Ising model with quenched disorder at T = 0T=0 in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents \nu_\mathrm{s}νs and \nu_\mathrm{w}νw as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent \betaβ and the critical exponent \nu_{\mathrm{av}}νav of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent z'z′ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

4He monolayer on graphene: a quantum Monte Carlo study

We revisit the problem of adsorption of a single 4He layer on graphene, focusing on the commensurate (C 1/3) crystalline phase, specifically on whether it may possess a nonzero superfluid response, and on the existence of superfluid phases, either (metastable) liquid or vacancy-doped crystalline. We make use of canonical quantum Monte Carlo simulations at zero and finite temperature, based on a realistic microscopic model of the system. Our results confirm the absence of any superfluid response in the commensurate crystal, and that no thermodynamically stable uniform phase exists at lower coverage. No evidence of a possibly long-lived, metastable superfluid phase at C 1/3 coverage is found. Altogether, the results of ground-state projection methods and finite-temperature simulations are entirely consistent.

Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge. Published by the American Physical Society 2024

Quantum scaling of the spin lattice relaxation rate in the checkerboard J-Q model

Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboard J-Q model by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergent O(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance, 1/T1 , exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature, 1/T1 rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas 1/T1 drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponent φ ≈ 0.3, consistent with the scaling ansatz ϕ=νz with ν ≈ 0.3 and z = 1. Near the quantum phase transition, the temperature dependent 1/T1 shows a broad crossover regime where a universal scaling 1/T1∼Tη with η ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.

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.

From structure to surface tension of small silicon clusters by Quantum Monte Carlo simulations

We investigate the structural, surface and electronic properties of small silicon clusters Sin (for n=2 to 15) using HF, DFT and FN-DMC calculations. We analyze the atomic configurations, surface properties and electronic structures and show that the radius and average surface area of the clusters can be modeled by a Jellium-type model. We found that the surface tension σ of the clusters decreases with increasing cluster size in the range of the clusters under investigation. An estimate of the surface tension for bulk silicon yields σbulk=0.88(3) J/m2 in agreement with recent experiments. The average bond length of the clusters shows a non-monotonic behavior. Smaller clusters exhibit a high spin state influenced by electron correlation, especially during the 2D to 3D structural transition, which occurs at n=4 to n=5. We also find that the Si4, Si10 and Si12 clusters exhibit enhanced stability due to electron correlation. Our results are consistent with the experiments on bond length, binding energy and dissociation energy.

Effective theory for graphene nanoribbons with junctions

Graphene nanoribbons are a promising candidate for fault-tolerant quantum electronics. In this scenario, qubits are realized by localized states that can emerge on junctions in hybrid ribbons formed by two armchair nanoribbons of different widths. We derive an effective theory based on a tight-binding ansatz for the description of hybrid nanoribbons and use it to make accurate predictions of the energy gap and nature of the localization in various hybrid nanoribbon geometries. We use quantum Monte Carlo simulations to demonstrate that the effective theory remains applicable in the presence of Hubbard interactions. We discover, in addition to the well-known localizations on junctions, which we call “Fuji”, a new type of “Kilimanjaro” localization smeared out over a segment of the hybrid ribbon. We show that Fuji localizations in hybrids of width N and N+2 armchair nanoribbons occur around symmetric junctions if and only if N(mod3)=1, while edge-aligned junctions never support strong localization. This behavior cannot be explained relying purely on the topological Z2 invariant, which has been believed to be the origin of the localizations to date. Published by the American Physical Society 2024

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.

Unconventional superconductivity and charge ordering in an extended ionic Hubbard model on the triangular lattice

To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d-wave and extended s-wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite-q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account.

Quantum Monte Carlo study of thin parahydrogen films on graphite

The low-temperature properties of one and two layers of parahydrogen adsorbed on graphite are investigated theoretically through Quantum Monte Carlo simulations. We adopt a microscopic model that explicitly includes the corrugation of the substrate. We study the phase diagram of a monolayer up to second layer promotion, and the possible occurrence of superfluidity in the second layer. We obtain results down to a temperature as low as 8 mK. We find second-layer promotion to occur at a considerably greater coverage than obtained in previous calculations and estimated experimentally; moreover, we find no evidence of a possible finite superfluid response in the second layer, disproving recent theoretical predictions.

Fourier-Matsubara series expansion for imaginary-time correlation functions.

A Fourier-Matsubara series expansion is derived for imaginary-time correlation functions that constitutes the imaginary-time generalization of the infinite Matsubara series for equal-time correlation functions. The expansion is consistent with all known exact properties of imaginary-time correlation functions and opens up new avenues for the utilization of quantum Monte Carlo simulation data. Moreover, the expansion drastically simplifies the computation of imaginary-time density-density correlation functions with the finite temperature version of the self-consistent dielectric formalism. Its existence underscores the utility of imaginary-time as a complementary domain for many-body physics.

Effective model for superconductivity in magic-angle graphene

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge 2e and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1)×Z2. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation. Published by the American Physical Society 2024

Suppression of polaron self-localization by correlations

We investigate self-localization of a polaron in a homogeneous Bose-Einstein condensate in one dimension. This effect, where an impurity is trapped by the deformation that it causes in the surrounding Bose gas, has been first predicted by mean-field calculations, but has not been seen in experiments. We study the system in one dimension, where, according to the mean-field approximation, the self-localization effect is particularly robust and present for arbitrarily weak impurity-boson interactions. We address the question whether self-localization is a real effect by developing a variational method which incorporates impurity-boson correlations nonperturbatively and solving the resulting inhomogeneous correlated polaron equations. We find that correlations inhibit self-localization except for very strongly repulsive or attractive impurity-boson interactions. Our prediction for the critical interaction strength for self-localization agrees with a sharp drop of the inverse effective mass found in quantum Monte Carlo simulations of polarons in one dimension. Published by the American Physical Society 2024

Magnetic short-range order and Griffiths-like phase in the S-1/2 spin-dimer ferromagnet BaCu(SeO3)2

The polycrystals of S = 1/2 spin-dimer compound BaCu(SeO3)2 have been synthesized by using solid-state reaction. Without long-range order, the magnetic susceptibility χ(T) curve presents two anomalies at T1 = 5 K and TG = 58 K due to antiferromagnetic (AFM) short-range order and short-range ferromagnetic (FM) correlations, respectively, which is further supported by the specific heat and electron spin resonance data. The high-temperature χ(T) curve follows the Curie-Weiss law with θCW = 11.3 K, showing the dominant intradimer FM interaction. The magnetization M(H) curve at 2 K is characteristic of an AFM-FM transition at 0.4 T, suggesting the weak interdimer AFM couplings. The density function theory calculations and quantum Monte Carlo simulations allow an estimation of the intradimer and interdimer exchanges with J1/kB = 39.09 K, J2/kB = −1.51 K, and J3/kB = −1.68 K. Interestingly, the χ−1(T) curve within θCW <T <TG deviates downward from paramagnetic Curie-Weiss behavior, mimicking the Griffiths-like phase. This is further supported by the ac magnetic susceptibility and magnetic relaxation measurements. The competing intradimer FM and interdimer AFM exchanges with a subtle ratio between them are proposed to be responsible for the formation of Griffiths-like phase.

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.