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Entanglement entropy in quantum spin chains with broken parity number symmetry

by Arash Jafarizadeh, M. A. Rajabpour

This Submission thread is now published as SciPost Phys. 12, 195 (2022)

Submission summary

As Contributors: Arash Jafarizadeh
Arxiv Link: https://arxiv.org/abs/2109.06359v3 (pdf)
Date accepted: 2022-06-01
Date submitted: 2022-05-19 18:44
Submitted by: Jafarizadeh, Arash
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational

Abstract

Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in-depth the properties of the eigenstates of the enlarged Hamiltonian. In particular, we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.

Published as SciPost Phys. 12, 195 (2022)



Submission & Refereeing History

Published as SciPost Phys. 12, 195 (2022)

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Resubmission 2109.06359v3 on 19 May 2022

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