Entanglement negativity via replica trick: a Quantum Monte Carlo approach

Abstract

Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. These quantities can serve as witnesses of criticality. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. These are more pronounced in the presence of boundaries. For large chains we find perfect agreement with CFT. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. Remarkably, the finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.

References in corpus (17)

• Area laws in quantum systems: mutual information and correlations
• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement Entropy and Twist Fields
• Unusual Corrections to Scaling in Entanglement Entropy
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Scaling of entanglement between separated blocks in spin chains at criticality
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Finite Temperature Critical Behavior of Mutual Information
• Entanglement, combinatorics and finite-size effects in spin-chains
• The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations

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