Entanglement entropy and conformal field theory

被引:1241
作者
Calabrese, Pasquale [1 ,2 ]
Cardy, John [3 ,4 ]
机构
[1] Univ Pisa, Dipartimento Fis, Pisa, Italy
[2] Ist Nazl Fis Nucl, Pisa, Italy
[3] Univ Oxford, Rudolf Peierls Ctr Theoret Phys, Oxford OX1 3NP, England
[4] Univ Oxford All Souls Coll, Oxford OX1 4AL, England
基金
英国工程与自然科学研究理事会;
关键词
CORNER TRANSFER-MATRICES; DENSITY-MATRICES; FREE-ENERGY; QUANTUM; BOUNDARY; XY; INVARIANCE; CHAIN; POINT;
D O I
10.1088/1751-8113/42/50/504005
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.
引用
收藏
页数:36
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共 170 条
  • [1] UNIVERSAL NONINTEGER GROUND-STATE DEGENERACY IN CRITICAL QUANTUM-SYSTEMS
    AFFLECK, I
    LUDWIG, AWW
    [J]. PHYSICAL REVIEW LETTERS, 1991, 67 (02) : 161 - 164
  • [2] UNIVERSAL TERM IN THE FREE-ENERGY AT A CRITICAL-POINT AND THE CONFORMAL ANOMALY
    AFFLECK, I
    [J]. PHYSICAL REVIEW LETTERS, 1986, 56 (07) : 746 - 748
  • [3] ALBA V, 2009, ARXIV09100706
  • [4] Magnetic and glassy transitions in the square-lattice XY model with random phase shifts
    Alba, Vincenzo
    Pelissetto, Andrea
    Vicari, Ettore
    [J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2010,
  • [5] Entanglement in many-body systems
    Amico, Luigi
    Fazio, Rosario
    Osterloh, Andreas
    Vedral, Vlatko
    [J]. REVIEWS OF MODERN PHYSICS, 2008, 80 (02) : 517 - 576
  • [6] Entanglement and magnetic order
    Amico, Luigi
    Fazio, Rosario
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (50)
  • [7] [Anonymous], 1986, Pisma Zh. Eksp. Teor. Fiz
  • [8] Near extremal black hole entropy as entanglement entropy via AdS2/CFT1
    Azeyanagi, Tatsuo
    Nishioka, Tatsuma
    Takayanagi, Tadashi
    [J]. PHYSICAL REVIEW D, 2008, 77 (06):
  • [9] Matrix Product States for Dynamical Simulation of Infinite Chains
    Banuls, M. C.
    Hastings, M. B.
    Verstraete, F.
    Cirac, J. I.
    [J]. PHYSICAL REVIEW LETTERS, 2009, 102 (24)
  • [10] Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
    Barthel, T.
    Kasztelan, C.
    McCulloch, I. P.
    Schollwoeck, U.
    [J]. PHYSICAL REVIEW A, 2009, 79 (05)