arXiv:cond-mat/0502034 · Journal of Physics A Mathematical and General

Entanglement entropy with interface defects

Ingo Peschel

Published May 3, 2005• 101 citations

Abstract

We consider a section of a half-filled chain of free electrons and its entanglement with the rest of the system in the presence of one or two interface defects. We find a logarithmic behaviour of the entanglement entropy with constants depending continuously on the defect strength.

DOI: 10.1088/0305-4470/38/20/002

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arXiv:cond-mat/0502034 · Journal of Physics A Mathematical and General

Entanglement entropy with interface defects

Ingo Peschel

Published May 3, 2005• 101 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/38/20/002

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The quantum Ising chain of length,

L

, which is separated into two parts by localized or extended defects is considered at the critical point where scaling of the interface magnetization is nonuniversal. We measure the entanglement entropy between the two halves of the system in equilibrium, as well as after a quench, when the interaction at the interface is changed for time

t>0

. For the localized defect the increase in the entropy with

\text{log}\text{ }L

or with

\text{log}\text{ }t

involves the same effective central charge, which is a continuous function of the strength of the defect. On the contrary for the extended defect the equilibrium entropy is saturated but the nonequilibrium entropy has a logarithmic time dependence the prefactor of which depends on the strength of the defect.

{\cal S}\sim \ln\ln(L)

, where

L

is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance

l

from the contact point as

\sim l^{-\kappa}

. For

\kappa<1/2

, the entropy scales as

{\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)

, while for

\kappa \ge 1/2

, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.