Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations

Abstract

Many-body entanglement unveils additional aspects of quantum matter and offers insights into strongly correlated physics. While ground-state entanglement has received much attention in the past decade, the study of mixed-state quantum entanglement using negativity in interacting fermionic systems remains largely unexplored. We demonstrate that the partially transposed density matrix of interacting fermions, similar to their reduced density matrix, can be expressed as a weighted sum of Gaussian states describing free fermions, enabling the calculation of rank-$n$ Rényi negativity within the determinant quantum Monte Carlo framework. We calculate the rank-two Rényi negativity for the half-filled Hubbard model and the spinless $t$-$V$ model. Our calculation reveals that the area law coefficient of the Rényi negativity for the spinless $t$-$V$ model has a logarithmic finite-size scaling at the finite-temperature transition point. Our work contributes to the calculation of entanglement and sets the stage for future studies on quantum entanglement in various fermionic many-body mixed states.

9+11 pages, 3+2 figures

References in corpus (18)

• Continuous-time Monte Carlo methods for quantum impurity models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement negativity in quantum field theory
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Finite temperature entanglement negativity in conformal field theory
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement negativity in the harmonic chain out of equilibrium
• On the partial transpose of fermionic Gaussian states
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Finite Temperature Critical Behavior of Mutual Information
• 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
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Entanglement negativity between separated regions in quantum critical systems
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Quasilocal entanglement across the Mott-Hubbard transition
• Delay Update in determinant quantum Monte Carlo

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• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• Bell sampling in Quantum Monte Carlo simulations