Entanglement Hamiltonian of Interacting Fermionic Models

Abstract

Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular) Hamiltonian has proven to be a considerably more difficult problem, and only a few results are available. We introduce a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations. We implement our method on the one-dimensional Hubbard chain partitioned into two segments and on the Hubbard two-leg ladder partitioned into two chains. In both cases, we study the evolution of the entanglement Hamiltonian as a function of the physical temperature.

9 pages, 5 figures including Supplemental Material; v2: new refs; v3: 10 pages, 5 figures including Supplemental Material, improved exposition, new refs; published version

References in corpus (14)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Entanglement hamiltonians in two-dimensional conformal field theory
• A User-Friendly Hybrid Sparse Matrix Class in C++
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• 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
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Entanglement Thermodynamics
• Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
• Entanglement Spectra of Heisenberg Ladders of higher Spin

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