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Title: Interfaces and the extended Hilbert space of Chern-Simons theory

Abstract

The low energy effective field theories of (2 + 1) dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In [1] the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics; Univ. of Amsterdam (Netherlands). Inst. of Physics
  2. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1646649
Alternate Identifier(s):
OSTI ID: 1779390; OSTI ID: 1843329
Grant/Contract Number:  
SC0019517
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons Theories; Gauge Symmetry; Topological Field Theories; Topological States of Matter; Chern Simons quantum entanglement interfaces

Citation Formats

Fliss, Jackson R., and Leigh, Robert G. Interfaces and the extended Hilbert space of Chern-Simons theory. United States: N. p., 2020. Web. doi:10.1007/JHEP07(2020)009.
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Fliss, Jackson R., & Leigh, Robert G. Interfaces and the extended Hilbert space of Chern-Simons theory. United States. https://doi.org/10.1007/JHEP07(2020)009
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Fliss, Jackson R., and Leigh, Robert G. Wed . "Interfaces and the extended Hilbert space of Chern-Simons theory". United States. https://doi.org/10.1007/JHEP07(2020)009. https://www.osti.gov/servlets/purl/1646649.
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@article{osti_1646649,
title = {Interfaces and the extended Hilbert space of Chern-Simons theory},
author = {Fliss, Jackson R. and Leigh, Robert G.},
abstractNote = {The low energy effective field theories of (2 + 1) dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In [1] the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.},
doi = {10.1007/JHEP07(2020)009},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2020,
place = {United States},
year = {Wed Jul 01 00:00:00 EDT 2020},
month = {Wed Jul 01 00:00:00 EDT 2020}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/JHEP07(2020)009
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Cited by: 5 works
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Figures / Tables:

Figure 1 Figure 1: On the left two Chern-Simons theories joined on an interface. Alternatively, once folded, this is a theory valued in the tensor sum with a hard boundary.
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    Multipartitioning topological phases by vertex states and quantum entanglement
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