Entanglement in fermionic chains with finite-range coupling and broken symmetries

被引：41

作者：

Ares, Filiberto ^{[1
]}

Esteve, Jose G. ^{[1
,2
]}

Falceto, Fernando ^{[1
,2
]}

de Queiroz, Amilcar R. ^{[1
,3
]}

机构：

[1] Univ Zaragoza, Dept Fis Teor, E-50009 Zaragoza, Spain

[2] Inst Biocomputac & Fis Sistemas Complejos BIFI, Zaragoza 50009, Spain

[3] Univ Brasilia, Inst Fis, BR-70919970 Brasilia, DF, Brazil

来源：

PHYSICAL REVIEW A | 2015年 / 92卷 / 04期

关键词：

QUANTUM SPIN CHAINS; TOEPLITZ DETERMINANTS; FIELD-THEORY; ENTROPY; MATRICES;

D O I：

10.1103/PhysRevA.92.042334

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of contiguous sites in the limit of large size. The present work generalizes similar results due to Its, Jin, and Korepin [Fields Institute Communications, Universality and Renormalization, Vol. 50, p. 151, 2007] and Its, Mezzadri, and Mo [Commun. Math. Phys. 284, 117 (2008)]. A striking feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size. This logarithmic behavior originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyze the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long-range pairing.

引用

页数：11

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