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Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations

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journal contribution
posted on 05.06.2017, 13:59 authored by Richard M. Cole, Frank Pollmann, Joseph BetourasJoseph Betouras
We study numerically the entanglement entropy and spatial correlations of the one dimensional transverse field Ising model with three different perturbations. First, we focus on the out of equilibrium, steady state with an energy current passing through the system. By employing a variety of matrix-product state based methods, we confirm the phase diagram and compute the entanglement entropy. Second, we consider a small perturbation that takes the system away from integrability and calculate the correlations, the central charge and the entanglement entropy. Third, we consider periodically weakened bonds, exploring the phase diagram and entanglement properties first in the situation when the weak and strong bonds alternate (period two-bonds) and then the general situation of a period of n bonds. In the latter case we find a critical weak bond that scales with the transverse field as $J'_c/J$ = $(h/J)^n$, where $J$ is the strength of the strong bond, $J'$ of the weak bond and $h$ the transverse field. We explicitly show that the energy current is not a conserved quantity in this case.

Funding

The work has been supported partly by EPSRC through grant EP/M006581/1 (JJB) and by Research Unit FOR 1807 through grants no. PO 1370/2-1 (FP)

History

School

  • Science

Department

  • Physics

Published in

Physical Review B - Condensed Matter and Materials Physics

Citation

COLE, R., POLLMAN, F. and BETOURAS, J.J., 2017. Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations. Physical Review B - Condensed Matter and Materials Physics, 95 (21), 214410.

Publisher

© American Physical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

17/05/2017

Publication date

2017-06-14

Notes

This paper was accepted for publication in the journal Physical Review B - Condensed Matter and Materials Physics and the definitive published version is available at https://doi.org/10.1103/PhysRevB.95.214410.

ISSN

0163-1829

Language

en

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