Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures

Abstract

We describe an approach for many-body calculations with a finite-temperature, grand canonical ensemble formalism using auxiliary-field quantum Monte Carlo (AFQMC) with a self-consistent constraint to control the sign problem. The usual AFQMC formalism of Blankenbecler, Scalapino, and Sugar suffers from the sign problem with most physical Hamiltonians, as is well known. Building on earlier ideas to constrain the paths in auxiliary-field space [Phys. Rev. Lett. \textbf{83}, 2777 (1999)] and incorporating recent developments in zero-temperature, canonical-ensemble methods, we discuss how a self-consistent constraint can be introduced in the finite-temperature, grand-canonical-ensemble framework. This together with several other algorithmic improvements discussed here leads to a more accurate, more efficient, and numerically more stable approach for finite-temperature calculations. We carry out a systematic benchmark study in the two-dimensional repulsive Hubbard model at $1/8$ doping. Temperatures as low as $T=1/80$ (in units of hopping) are reached. The finite-temperature method is exact at very high temperatures, and approaches the result of the zero-temperature constrained-path AFQMC as temperature is lowered. The benchmark shows that systematically accurate results are obtained for thermodynamic properties.

arXiv comment17 pages, 7 figures

References in corpus (42)

• Quantum Monte Carlo methods for nuclear physics
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• A Constrained Path Monte Carlo Method for Fermion Ground States
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Neel order in square and triangular lattice Heisenberg models
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• A Constrained Path Quantum Monte Carlo Method for Fermion Ground States
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Four - Fermi Theories in Fewer Than Four Dimensions
• Pairing Correlations in the Two-Dimensional Hubbard Model
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Observation of 2D fermionic Mott insulators of ${}^{40}$K with single-site resolution
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Equation of state of the two-dimensional Hubbard model
• The fermion bag approach to lattice field theories
• Spin and charge order in doped Hubbard model: long-wavelength collective modes
• Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
• Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations
• Solution to sign problems in half-filled spin-polarized electronic systems
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules
• Finite-Temperature Monte Carlo Calculations For Systems With Fermions
• Pairing on striped $t$-$t^{\prime }$-$J$ lattices
• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems
• Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
• Infinite Variance in Fermion Quantum Monte Carlo Calculations
• Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo
• Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model
• Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo
• Ab Initio Models of Dislocations
• Finite-Temperature Auxiliary-Field Quantum Monte Carlo for Bose-Fermi Mixtures
• Solution to sign problems in models of interacting fermions and quantum spins
• Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model

Cited by in corpus (38)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
• Quantum Critical Points and the Sign Problem
• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• A neutral-atom Hubbard quantum simulator in the cryogenic regime
• Reaching the continuum limit in finite-temperature ab initio field-theory computations in many-fermion systems
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Fermi Arcs From Dynamical Variational Monte Carlo
• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model
• Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo
• Deconvolving the components of the sign problem
• Improved modularity and new features in ipie: Toward even larger AFQMC calculations on CPUs and GPUs at zero and finite temperatures
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• Interfacing branching random walks with Metropolis sampling: constraint release in auxiliary-field quantum Monte Carlo
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers
• A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo
• Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators
• Nature of the mixed-parity pairing of attractive fermions with spin-orbit coupling in optical lattice
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Implementing advanced trial wave functions in fermion quantum Monte Carlo via stochastic sampling
• Piecewise Interaction Picture Density Matrix Quantum Monte Carlo
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Addressing general measurements in quantum Monte Carlo
• Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
• Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model
• Spin-triplet pairing instability in a two-dimensional repulsive Hubbard model