One-particle entanglement for one dimensional spinless fermions after an interaction quantum quench

Matthias Thamm, Harini Radhakrishnan, Hatem Barghathi, Bernd Rosenow, and Adrian Del Maestro

arXiv:2206.11301

Abstract

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time dependent density matrix renormalization group calculations, we numerically compute the one body reduced density matrix for the $J$-$V$ model, as well as its post-quench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

Description

This repository includes links, code, scripts, and data to generate the figures in the paper.

Requirements

The data in this project was generated via exact diagonalization and dmrg.
Everything included in the data directory was generated via:

• ED equilibrium code
• ED quench code
• DMRG equilibrium and quench code

Support

M.T. and B.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. 406116891 within the Research Training Group RTG 2522/1 and under grant RO 2247/11-1. The creation of these materials was supported in part by the NSF under Grant No. DMR-2041995.

Figures

Figure 01: Interaction dependence of one particle von Neumann entanglement entropies

Figure 02: Waiting time dependence of eigenvalues of one body density after quench

Figure 03: Distribution function after quantum quench

Figure 04: Distribution function from LL result

Figure 05: Equilibrium one-particle entanglement entropy and phases of J-V model from DMRG results

Figure 06: Finite size scaling of equilibrium one-particle entanglement entropy

Figure 07: Comparing numerical equilibrium one-particle entanglement to LL result in the thermodynamic limit

Figure 08: Effective interaction cutoff in the equilibrium case

Figure 09: Post quench LL steady state limit

Figure 10: Evolution of one-particle entanglement after the quench

Figure 11: Finite size scaling of the steady state one-particle von Neumann entanglement entropy after the quench

Figure 12: Comparing numerical steady state one-particle entanglement to LL result in the thermodynamic limit after a quench

Figure 13: Interaction dependence of the effective cutoff

Figure 14: Time evolution of distribution function

Figure 15: Comparison time average of distribution function and equilibrium case

Figure 16: Distribution function after quantum quench to CDW phase