An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation

Abstract

Exponential observables, formulated as $\log ⟨e^{\hat{X}}⟩$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement entropy. Given that $e^X$ becomes exponentially large (or small) in the thermodynamic limit, accurately computing the expectation value of this exponential quantity presents a significant challenge. In this Letter, we propose a comprehensive algorithm for quantifying these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo (DQMC) method. We have applied this novel algorithm to the 2D half-filled Hubbard model. At the strong coupling limit, our method showcases a significant accuracy improvement compared to conventional methods that are derived from the internal energy. We also illustrate that this novel approach delivers highly efficient and precise measurements of the nth Rényi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be easily generalized to other models.

5 pages, 2 figure

References in corpus (45)

• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Quantum entanglement in condensed matter systems
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Universal terms for the entanglement entropy in 2+1 dimensions
• Entanglement Entropy and the Fermi Surface
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
• Scaling of entanglement entropy at deconfined quantum criticality
• Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Entanglement entropy from nonequilibrium work
• The Gross-Neveu-Yukawa Archipelago
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Topological Disorder Parameter
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Universal features of entanglement entropy in the honeycomb Hubbard model
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Entanglement, noise, and the cumulant expansion
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Universality and Critical Exponents of the Fermion Sign Problem
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
• Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• Bilayer Hubbard model: Analysis based on the fermionic sign problem
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Deconvolving the components of the sign problem
• Emus live on the Gross-Neveu-Yukawa archipelago

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