Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
arXiv:1605.09421 · doi:10.1103/PhysRevB.94.085103
Abstract
Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/t from 2 to 8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75, and 0.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasi-random sequences, which improves the convergence to the thermodynamic limit over pseudo-random and other sequences. With it and a careful finite size scaling analysis, we are able to obtain accurate values of ground state properties in the thermodynamic limit. Detailed results for finite-sized systems up to 16 \times 16 are also provided for benchmark purposes.
Published version, 14 pages, 9 figures, 4 tables
References in corpus (13)
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Theory of Intertwined Orders in High Temperature Superconductors
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- The Finite Size Error in Many-body Simulations with long-Ranged Interactions
- Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
- Finite-size correction in many-body electronic structure calculations
- Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
- Exact Numerical Results on the Ground State of Strongly Interacting Fermi Gases in Two Dimensions
- Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
- Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2
- Infinite Variance in Fermion Quantum Monte Carlo Calculations
- Spin Density Waves in the Hubbard model - A DMFT approach
- CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations
Cited by in corpus (74)
- Stripe order in the underdoped region of the two-dimensional Hubbard model
- The Hubbard model: A computational perspective
- Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
- Absence of superconductivity in the pure two-dimensional Hubbard model
- Coexistence of superconductivity with partially filled stripes in the Hubbard model
- Fermionic Wave Functions from Neural-Network Constrained Hidden States
- Plaquette versus ordinary -wave pairing in the -Hubbard model on a width 4 cylinder
- Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
- Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures
- Variational Benchmarks for Quantum Many-Body Problems
- Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
- Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method
- Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting
- Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo
- Hidden Mott transition and large- superconductivity in the two-dimensional Hubbard model
- Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
- Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
- Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model
- Transcorrelated Density Matrix Renormalization Group
- Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide
- Solution of the "sign problem" for the half filled Hubbard-Holstein model
- Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling
- Particle-hole asymmetry in the dynamical spin and charge structure factors of the corner-shared one-dimensional cuprates
- An efficient method for strongly correlated electrons in two-dimensions
- An efficient method for strongly correlated electrons in one dimension
- Metal-insulator transition in the ground-state of the three-band Hubbard model at half-filling
- Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
- Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations
- Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
- Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations
- Robust superconducting correlation against inter-site interactions in the extended two-leg Hubbard ladder
- Phase transitions in partial summation methods: Results from the 3D Hubbard model
- Gaussian Process States: A data-driven representation of quantum many-body physics
- Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
- Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain walls
- Magnetic and charge orders in the ground state of the Emery model -- accurate numerical results
- Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
- Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
- Giant Magnetoresistance in Hubbard Chains
- Study of the superconducting order parameter in the negative- 2D-Hubbard model by grand-canonical twist-averaged boundary conditions
- Toward an accurate equation of state and B1-B2 phase boundary for magnesium oxide to TPa pressures and eV temperatures
- Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
- Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model
- Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
- Autoregressive neural quantum states of Fermi Hubbard models
- Algorithm for branching and population control in correlated sampling
- Accurate computations of Rashba spin-orbit coupling in interacting systems: from the Fermi gas to real materials
- Polaronic correlations from optimized ancilla wave functions for the Fermi-Hubbard model
- A numerically exact study of Weyl superconductivity
- Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions
- Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators
- Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems
- Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions
- Response functions for the two-dimensional ultracold Fermi gas: dynamical BCS theory and beyond
- Auxiliary Field Quantum Monte Carlo for Dilute Neutrons on the Lattice
- Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
- Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model
- Critical gate distance for Wigner crystallization in the two-dimensional electron gas
- The Fractal-Lattice Hubbard Model
- Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
- Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
- Enhanced Twist-Averaging Technique for Magnetic Metals: Applications using Quantum Monte Carlo
- Superconducting qubits in the millions: the potential and limitations of modularity
- Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections
- Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
- Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo
- Investigating Stark many-body localization with continuous unitary transformation flows
- The light-matter correlation energy functional of the cavity-coupled two-dimensional electron gas via quantum Monte Carlo simulations
- Efficient Fermi-Hubbard model ground-state preparation by coupling to a classical reservoir in the instantaneous-response limit
- Scaling up the transcorrelated density matrix renormalization group
- Addressing the Infinite Variance Problem in Fermionic Monte Carlo Simulations: Retrospective Error Remediation and the Exact Bridge Link Method
- Tuning superconducting pairing symmetry via a staggered potential in the doped honeycomb Hubbard model
- Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
- Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model