Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo

Abstract

We present a method for improving measurements of the entanglement Rényi entropies in quantum Monte Carlo simulations by relating them with measurements of participation Rényi entropies. Exploiting the capability of building improved estimators for the latter allows to obtain very good estimates for entanglement Rényi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated providing access to the thermodynamic Rényi entropies with high accuracy. We also explore a recently-proposed method for the reconstruction of the entanglement spectrum from entanglement Rényi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal Rényi entropies.

15 pages, 11 figures

References in corpus (11)

• The ALPS project release 1.3: open source software for strongly correlated systems
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Rényi entropy of a line in two-dimensional Ising models
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Valence Bond Entanglement Entropy
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Entanglement Spectra of Heisenberg Ladders of higher Spin

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