Universal features of entanglement entropy in the honeycomb Hubbard model

Abstract

The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal features have yet to be observed. In this paper we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum Monte Carlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at $T=0$. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.

Published version. Added new triangular subsystem with corner logarithm versus U

References in corpus (19)

• Interactions and phase transitions on graphene's honeycomb lattice
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Universal terms for the entanglement entropy in 2+1 dimensions
• Universality of corner entanglement in conformal field theories
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Scaling of entanglement entropy at deconfined quantum criticality
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• 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
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Cornering the universal shape of fluctuations
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems

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• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
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• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Quasilocal entanglement across the Mott-Hubbard transition
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Residual entropy from temperature incremental Monte Carlo method
• Entanglement in the pseudogap regime of cuprate superconductors
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• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
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