Entanglement entropy, quantum fluctuations, and thermal entropy in topological phases
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Springer
Received: February 4, 2019 Accepted: April 30, 2019 Published: May 20, 2019
Entanglement entropy, quantum fluctuations, and thermal entropy in topological phases
a
Department of Physics and Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China b State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China c Department of Physics, Center for Field Theory and Particle Physics, and Institute for Nanoelectronic devices and Quantum computing, Fudan University, Shanghai 200433, China d Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China e Collaborative Innovation Center of Advanced Microstructures, Nanjing, 210093, China
E-mail: [email protected], [email protected] Abstract: Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective — the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system encodes the quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries. Keywords: Topological States of Matter, Anyons, Topological Field Theories ArXiv ePrint: 1901.09033 1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)110
JHEP05(2019)110
Yuting Hua,b,d,1 and Yidun Wanb,c,d,a,e,1
Contents 1 Introduction
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2 Quantum double model and holonomy bases 2.1 Observables 2.2 Holonomy bases: a non-local transformation
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4 Topological orders with gapped physical boundaries 4.1 Cylinder case I 4.1.1 The fusion basis 4.2 Cylinder case II 4.2.1 The fusion basis 4.3 Generic cases 4.3.1 The disk case
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5 Discussions
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A Fusion basis in the sphere case
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B Reduced density matrix in cylinder case I
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C Reduced density matrix in cylinder case II
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D Some useful identities
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E Examples
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Introduction
Matter phases with intrinsic topological orders, or topological orders for short, are exotic, gapped phases of matter beyond the Landau-Ginzburg paradigm [1–7]. They not only have expanded our knowledge of phases of matter but also have important applications, including robust quantum memories and topological quantum computers [5, 8].
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JHEP05(2019)110
3 Fusion basis and the quasiparticle picture of entanglement 3.1 Entanglement entropy on a sphere in a holonomy basis 3.2 Fusion bases 3.3 Entanglement measures quasiparti
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