Entropy growth of shift-invariant states on a quantum spin chain

M. Fannes, B. Haegeman, M. Mosonyi

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We study the entropy of pure shift-invariant states on a quantum spin chain. Unlike the classical case, the local restrictions to intervals of length N are typically mixed and have therefore a nonzero entropy SN which is, moreover, monotonically increasing in N. We are interested in the asymptotics of the total entropy. We investigate in detail a class of states derived from quasi-free states on a CAR algebra. These are characterized by a measurable subset of the unit interval. As the entropy density is known to vanish, SN is sublinear in N. For states corresponding to unions of finitely many intervals, SN is shown to grow slower than log 2 N Numerical calculations suggest a log N behavior. For the case with infinitely many intervals, we present a class of states for which the entropy SN increases as Nα where α can take any value in (0,1).

Original languageEnglish
Pages (from-to)6005-6019
Number of pages15
JournalJournal of Mathematical Physics
Volume44
Issue number12
DOIs
Publication statusPublished - Dec 2003

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Quantum Spin Chain
Entropy
entropy
Invariant
shift
intervals
Interval
unions
Numerical Calculation
set theory
Vanish
constrictions
algebra
Union
Restriction
Algebra
Unit
Subset

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Entropy growth of shift-invariant states on a quantum spin chain. / Fannes, M.; Haegeman, B.; Mosonyi, M.

In: Journal of Mathematical Physics, Vol. 44, No. 12, 12.2003, p. 6005-6019.

Research output: Contribution to journalArticle

Fannes, M. ; Haegeman, B. ; Mosonyi, M. / Entropy growth of shift-invariant states on a quantum spin chain. In: Journal of Mathematical Physics. 2003 ; Vol. 44, No. 12. pp. 6005-6019.
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