Cornering Gapless Quantum States via Their Torus Entanglement

被引：14

作者：

Witczak-Krempa, William ^{[1
,4
]}

Sierens, Lauren E. Hayward ^{[2
,3
]}

Melko, Roger G. ^{[2
,3
]}

机构：

[1] Harvard Univ, Dept Phys, Cambridge, MA 02138 USA

[2] Univ Waterloo, Dept Phys & Astron, Waterloo, ON N2L 3G1, Canada

[3] Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada

[4] Univ Montreal, Dept Phys, Montreal, PQ H3C 3J7, Canada

来源：

PHYSICAL REVIEW LETTERS | 2017年 / 118卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

TOPOLOGICAL ORDER; ENTROPY;

D O I：

10.1103/PhysRevLett.118.077202

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by chi. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of chi and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for chi in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansatze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansatze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.

引用

页数：6

共 53 条

[31] Entanglement at a Two-Dimensional Quantum Critical Point: A Numerical Linked-Cluster Expansion Study [J].

Kallin, Ann B. ;

Hyatt, Katharine ;

Singh, Rajiv R. P. ;

Melko, Roger G. .

PHYSICAL REVIEW LETTERS, 2013, 110 (13)

[32] Anyons in an exactly solved model and beyond [J].

Kitaev, A .

ANNALS OF PHYSICS, 2006, 321 (01) :2-111

[33] Detecting Goldstone modes with entanglement entropy [J].

Kulchytskyy, Bohdan ;

Herdman, C. M. ;

Inglis, Stephen ;

Melko, Roger G. .

PHYSICAL REVIEW B, 2015, 92 (11)

[34] Quantum entanglement in condensed matter systems [J].

Laflorencie, Nicolas .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2016, 646 :1-59

[35] Spin-wave approach for entanglement entropies of the J1-J2 Heisenberg antiferromagnet on the square lattice [J].

Laflorencie, Nicolas ;

Luitz, David J. ;

Alet, Fabien .

PHYSICAL REVIEW B, 2015, 92 (11)

[36]

Lieb E. H., 1973, J MATH PHYS N, V14

[37] Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries [J].

Luitz, David J. ;

Plat, Xavier ;

Alet, Fabien ;

Laflorencie, Nicolas .

PHYSICAL REVIEW B, 2015, 91 (15)

[38]

Metlitski M.A., ARXIV11125166

[39] Entanglement entropy in the O(N) model [J].

Metlitski, Max A. ;

Fuertes, Carlos A. ;

Sachdev, Subir .

PHYSICAL REVIEW B, 2009, 80 (11)

[40] Seeing a c-theorem with holography [J].

Myers, Robert C. ;

Sinha, Aninda .

PHYSICAL REVIEW D, 2010, 82 (04)

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