Valence bond entanglement entropy

被引：53

作者：

Alet, Fabien ^{[1
]}

Capponi, Sylvain

Laflorencie, Nicolas

Mambrini, Matthieu

机构：

[1] Univ Toulouse 3, IRSAMC, CNRS, Phys Theor Lab, F-31062 Toulouse, France

[2] Ecole Polytech Fed Lausanne, Inst Theoret Phys, CH-1015 Lausanne, Switzerland

来源：

PHYSICAL REVIEW LETTERS | 2007年 / 99卷 / 11期

关键词：

D O I：

10.1103/PhysRevLett.99.117204

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Neel phase.

引用

页数：4

共 42 条

[1] The ALPS Project: Open Source Software for Strongly Correlated Systems [J].

Alet, F. ;

Dayal, P. ;

Grzesik, A. ;

Honecker, A. ;

Koerner, M. ;

Laeuchli, A. ;

Manmana, S. R. ;

McCulloch, I. P. ;

Michel, F. ;

Noack, R. M. ;

Schmid, G. ;

Schollwoeck, U. ;

Stoeckli, F. ;

Todo, S. ;

Trebst, S. ;

Troyer, M. ;

Werner, P. ;

Wessel, S. .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2005, 74 :30-35

[2]

AMICO L, ARXIVQUANTPH0703044

[3] Entanglement scaling in critical two-dimensional fermionic and bosonic systems [J].

Barthel, T. ;

Chung, M. -C. ;

Schollwoeck, U. .

PHYSICAL REVIEW A, 2006, 74 (02)

[4] Some formal results for the valence bond basis [J].

Beach, K. S. D. ;

Sandvik, Anders W. .

NUCLEAR PHYSICS B, 2006, 750 (03) :142-178

[5] Valence bond solid phases in a cubic antiferromagnet [J].

Beach, K. S. D. ;

Sandvik, Anders W. .

PHYSICAL REVIEW LETTERS, 2007, 99 (04)

[6] Concentrating partial entanglement by local operations [J].

Bennett, CH ;

Bernstein, HJ ;

Popescu, S ;

Schumacher, B .

PHYSICAL REVIEW A, 1996, 53 (04) :2046-2052

[7] Entanglement entropy and quantum field theory [J].

Calabrese, P ;

Cardy, J .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2004,

[8] Statistics dependence of the entanglement entropy [J].

Cramer, M. ;

Eisert, J. ;

Plenio, M. B. .

PHYSICAL REVIEW LETTERS, 2007, 98 (22)

[9] Entanglement-area law for general bosonic harmonic lattice systems [J].

Cramer, M ;

Eisert, J ;

Plenio, MB ;

Dreissig, J .

PHYSICAL REVIEW A, 2006, 73 (01)

[10] LOW-TEMPERATURE PROPERTIES OF THE RANDOM HEISENBERG ANTI-FERROMAGNETIC CHAIN [J].

DASGUPTA, C ;

MA, S .

PHYSICAL REVIEW B, 1980, 22 (03) :1305-1319

← 1 2 3 4 5 →