Entanglement Spectroscopy using Quantum Monte Carlo

Abstract

We present a numerical scheme to reconstruct a subset of the entanglement spectrum of quantum many body systems using quantum Monte Carlo. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasi-degeneracy of the entanglement spectrum in the Haldane-Insulator phase. In general the method is able to reconstruct the largest few eigenvalues in each symmetry sector and typically performs better when the eigenvalues are not too different.

4+ pages, 3 figures

References in corpus (17)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Identifying Topological Order by Entanglement Entropy
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Hidden order in 1D Bose insulators
• Rise and fall of hidden string order of lattice bosons
• Entanglement entropy of critical spin liquids
• Phase diagram of the extended Bose Hubbard model
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Renyi Entropy of the Interacting Fermi Liquid
• Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates
• Competing Supersolid and Haldane Insulator phases in the extended one-dimensional bosonic Hubbard model
• Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

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• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• A path integral Monte Carlo method for Rényi entanglement entropies
• Rényi entropies of generic thermodynamic macrostates in integrable systems
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• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
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• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Quantum state tomography on a plaquette in the 2D Hubbard model
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study