The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter

Abstract

The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC) simulations of fermions are severely restricted by the notorious fermion sign problem (FSP). In this work, we present a hands-on discussion of the FSP and investigate in detail its manifestation with respect to temperature, system size, interaction-strength and -type, and the dimensionality of the system. Moreover, we analyze the probability distribution of fermionic expectation values, which can be non-Gaussian and fat-tailed when the FSP is severe. As a practical application, we consider electrons and dipolar atoms in a harmonic confinement, and the uniform electron gas in the warm dense matter regime. In addition, we provide extensive PIMC data, which can be used as a reference for the development of new methods and as a benchmark for approximations.

References in corpus (61)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• Wigner Crystallization in mesoscopic 2D electron systems
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• The Uniform Electron Gas at Warm Dense Matter Conditions
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• FPEOS: A First-Principles Equation of State Table of Deuterium for Inertial Confinement Fusion Applications
• Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
• Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of Brown Dwarfs
• \textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter
• Probing the interiors of the ice giants: Shock compression of water to 700 GPa and 3.8 g/ccm
• Ab initio thermodynamic results for the degenerate electron gas at finite temperature
• Excitation spectrum of a supersolid
• On the formation of Wigner molecules in small quantum dots
• Path-integral Monte Carlo study on a droplet of a dipolar Bose-Einstein condensate stabilized by quantum fluctuation
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Structure, superfluidity, and quantum melting of hydrogen clusters
• Ab-initio low-energy dynamics of superfluid and solid 4He
• Accurate exchange-correlation energies for the warm dense electron gas
• Density matrix quantum Monte Carlo
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Critical Temperature Curve in the BEC-BCS Crossover
• Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas
• Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas
• High order Chin actions in path integral Monte Carlo
• Interaction Picture Density Matrix Quantum Monte Carlo
• Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo
• Hexatic and mesoscopic phases in the 2D quantum Coulomb system
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes
• Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature
• \emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes II: Unpolarized Case
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Krylov-projected quantum Monte Carlo
• Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model
• Wigner molecules in quantum dots
• Path Integral Monte Carlo Simulation of Degenerate Electrons: Permutation-Cycle Properties
• Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas
• Exact wave functions of two-electron quantum rings
• Permutation Blocking Path Integral Monte Carlo approach to the Static Density Response of the Warm Dense Electron Gas
• Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo
• Dilute Bose gas with correlated disorder: A Path Integral Monte Carlo study
• Liquid metallic hydrogen and the structure of brown dwarfs and giant planets
• Collective and single-particle excitations in 2D dipolar Bose gases
• \textit{Ab Initio} results for the Static Structure Factor of the Warm Dense Electron Gas
• Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
• Uniform electron gases. I. Electrons on a ring
• Correlation effects and collective excitations in bosonic bilayers: role of quantum statistics, superfluidity and dimerization transition
• Uniform electron gases
• The Curse of Dimensionality for Numerical Integration of Smooth Functions
• Wigner molecules in polygonal quantum dots: A density functional study
• Superfluidity of strongly correlated bosons in two- and three-dimensional traps
• Finite temperature properties of strongly correlated systems via variational Monte Carlo
• A comparison between methods of analytical continuation for bosonic functions

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• Ab initio simulation of warm dense matter
• The Static Local Field Correction of the Warm Dense Electron Gas: An ab Initio Path Integral Monte Carlo Study and Machine Learning Representation
• Electronic Density Response of Warm Dense Matter
• Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory
• First principles simulations of dense hydrogen
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• Fast and Universal Kohn Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma
• Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation
• The Strongly Coupled Electron Liquid: ab initio Path Integral Monte Carlo Simulations and Dielectric Theories
• Dynamic properties of the warm dense electron gas: an ab initio path integral Monte Carlo approach
• Path Integral Monte Carlo Simulation of Degenerate Electrons: Permutation-Cycle Properties
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• Quantum Simulation of the Bosonic Creutz Ladder with a Parametric Cavity
• Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics
• Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality
• Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas
• Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
• Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature without fixed nodes
• Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte-Carlo simulations
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• Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations
• On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
• Overcoming finite-size effects in electronic structure simulations at extreme conditions
• The Relevance of Electronic Perturbations in the Warm Dense Electron Gas
• Screening of a test charge in a free-electron gas at warm dense matter and dense non-ideal plasma conditions
• Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions
• Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations
• Momentum distribution function and short-range correlations of the warm dense electron gas -- ab initio quantum Monte Carlo results
• Ab initio path integral Monte Carlo simulation of the Uniform Electron Gas in the High Energy Density Regime
• Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble
• Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange--correlation kernels
• Integral equation theory based dielectric scheme for strongly coupled electron liquids
• Classical bridge functions in classical and quantum plasma liquids
• Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
• Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions
• Prediction of a roton-type feature in warm dense hydrogen
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons
• Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter
• Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids
• The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory
• On the thermodynamics of fermions at any temperature based on parametrized partition function
• From Density Response to Energy Functionals and Back: An ab initio perspective on Matter Under Extreme Conditions
• Model-free Rayleigh weight from x-ray Thomson scattering measurements
• Towards a Quantum Fluid Theory of Correlated Many-Fermion Systems from First Principles
• Thermal Signals from Collective Electronic Excitations in Inhomogeneous Warm Dense Matter
• Determining QMC simulability with geometric phases
• Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter
• Ab initio Path Integral Monte Carlo Simulations of Quantum Dipole Systems in Traps: Superfluidity, Quantum Statistics, and Structural Properties
• Normal liquid ${}^3$He studied by Path Integral Monte Carlo with a parametrized partition function
• One--Component Plasma of a Million Particles via angular--averaged Ewald potential: A Monte Carlo study
• Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid
• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
• Path integral molecular dynamics simulations for Green's function in a system of identical bosons
• Accelerated free energy estimation in ab initio path integral Monte Carlo simulations
• Abnormal superfluid fraction and structural properties of electrons in 2D and 3D quantum dots: an ab initio path-integral Monte Carlo study
• Modelling of warm dense hydrogen via explicit real time electron dynamics: Dynamic structure factors
• Path integral molecular dynamics for thermodynamics and Green's function of ultracold spinor bosons
• Virial coefficients of the Uniform Electron Gas from Path Integral Monte Carlo Simulations
• Energy response and spatial alignment of the perturbed electron gas
• Path integral simulation of exchange interactions in CMOS spin qubits
• GPU acceleration of ab initio simulations of large-scale identical particles based on path integral molecular dynamics
• Dynamic properties of the warm dense uniform electron gas with the qSTLS dielectric scheme
• Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations
• Momentum distribution of the Uniform Electron Gas at finite temperature: Effects of spin-polarization
• A Machine-Learning Surrogate Model for ab initio Electronic Correlations at Extreme Conditions
• Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Piecewise Interaction Picture Density Matrix Quantum Monte Carlo
• Momentum distribution of He-3 in one dimension
• A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles
• Wick rotation derivation for weak values of the density and time-dependent density functional theory
• Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling
• PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
• Path Integral Monte Carlo Simulations of liquid ${}^3$He without Fixed Nodes: Structural Properties and Collective Excitations