Entanglement, noise, and the cumulant expansion

Abstract

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate lognormal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the $n$-th Rényi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4,\dots ,10$ Rényi entropies of the 1D attractive Hubbard model. We use that data to extrapolate to the von Neumann ($n=1$) and $n\to \infty$ cases.

Significantly expanded manuscript; improved presentation, new data and figures, new approach to the calculation of $n>2$ Rényi entropies. 8 pages, 8 figures

References in corpus (11)

• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Finite Temperature Critical Behavior of Mutual Information
• Renyi Entropy of the Interacting Fermi Liquid
• The ground state energy at unitarity
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

Cited by in corpus (21)

• Quantum entanglement in condensed matter systems
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Entanglement Hamiltonian of Interacting Fermionic Models
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• On the Statistics of Baryon Correlation Functions in Lattice QCD
• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• Path integral contour deformations for noisy observables
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion
• Kondo Breakdown via Fractionalization in a Frustrated Kondo Lattice Model
• Estimating the central charge from the Rényi entanglement entropy
• Phase Unwrapping and One-Dimensional Sign Problems
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Tan's contact and the phase distribution of repulsive Fermi gases: Insights from QCD noise analyses
• Mutual information in heavy-fermion systems
• Particle partition entanglement of one dimensional spinless fermions
• An analog of topological entanglement entropy for mixed states
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions
• Large-time correlation functions in bosonic lattice field theories
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Entanglement studies of interacting fermionic models