Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

Abstract

Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard problem and any generic solution thus highly elusive, the Monte Carlo sampling of interacting many-fermion systems is commonly thought to be restricted to a small class of model systems for which a sign-free basis has been identified. Here we demonstrate that entanglement measures, in particular the so-called Renyi entropies, can intrinsically exhibit a certain robustness against the sign problem in auxiliary-field quantum Monte Carlo approaches and possibly allow for the identification of global ground-state properties via their scaling behavior even in the presence of a strong sign problem. We corroborate these findings via numerical simulations of fermionic quantum phase transitions of spinless fermions on the honeycomb lattice at and below half-filling.

References in corpus (16)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Continuous-time Monte Carlo methods for quantum impurity models
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Entanglement entropy of critical spin liquids
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• A path integral Monte Carlo method for Rényi entanglement entropies
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

Cited by in corpus (12)

• Machine learning quantum phases of matter beyond the fermion sign problem
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Mitigating the fermion sign problem by automatic differentiation
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• The statistical mechanics and machine learning of the $\alpha$-Rényi ensemble