Entanglement entropy and the complex plane of replicas

Gliozzi, Ferdinando and Tagliacozzo, Luca (2010) Entanglement entropy and the complex plane of replicas. Journal of Statistical Mechanics: Theory and Experiment, 2010 1: P01002-1-P01002-21. doi:10.1088/1742-5468/2010/01/P01002

Author Gliozzi, Ferdinando
Tagliacozzo, Luca
Title Entanglement entropy and the complex plane of replicas
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2010-01
Sub-type Article (original research)
DOI 10.1088/1742-5468/2010/01/P01002
Volume 2010
Issue 1
Start page P01002-1
End page P01002-21
Total pages 21
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2011
Language eng
Formatted abstract
The entanglement entropy of a subsystem A of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the nth power of the reduced density matrix trρnA. We study the analytic properties of this quantity as a function of n in some quantum critical Ising-like models in 1+1 and 2+1 dimensions. Although we find no true singularities for n>0, there is a threshold value of n close to 2 which separates two very different 'phases'. The region with larger n is characterized by rapidly convergent Taylor expansions and is very smooth. The region with smaller n has a very rich and varied structure in the complex n plane and is characterized by Taylor coefficients which instead of being monotone decreasing, have a maximum growing with the size of the subsystem. Finite truncations of the Taylor expansion in this region lead to increasingly poor approximations of trρnA. The computation of the entanglement entropy from the knowledge of trρnA for positive integer n becomes extremely difficult, particularly in spatial dimensions larger than 1, where one cannot use conformal field theory as a guidance in the extrapolations to n = 1.
© IOP Publishing Ltd.
Keyword Spin chains
Ladders and planes (theory)
Quantum phase transitions (theory)
Entanglement in extended quantum systems (theory)
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article # P01002

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2011 Collection
School of Physical Sciences Publications
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Citation counts: TR Web of Science Citation Count  Cited 16 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 9 times in Scopus Article | Citations
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Created: Sun, 21 Feb 2010, 00:03:09 EST