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Title: Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter

Abstract

The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly solvable models for a plethora of gapped quantum phases of matter. Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak local perturbations thus allows us to develop a general framework within which the entanglement features of gapped topological phases can be computed and contrasted. In particular, we study models harboring fracton order, both type-I and type-II, and compare the resulting ES with that of both conventional topological order and of (strong) subsystem symmetry protected topological (SSPT) states. We find that nonlocal surface stabilizers (NLSS), a set of symmetries of the Hamiltonian which form on the boundary of the entanglement cut, act as purveyors of universal nonlocal features appearing in the entanglement spectrum. While in conventional topological orders and fracton orders, the NLSS retain a form of topological invariance with respect to the entanglement cut, subsystem symmetric systems—fracton and SSPT phases—additionally show a nontrivial geometric dependence on the entanglement cut, corresponding to the subsystem symmetry. This sheds further light on the interplay between geometricmore » and topological effects in fracton phases of matter and demonstrates that strong SSPT phases harbour a measure of quasilocal entanglement beyond that encountered in conventional SPT phases. Here, we further show that a version of the edge-entanglement correspondence, established earlier for gapped two-dimensional topological phases, also holds for gapped three-dimensional fracton models.« less

Authors:
 [1];  [1];  [2]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. Princeton Univ., NJ (United States)
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1612178
Alternate Identifier(s):
OSTI ID: 1511510
Grant/Contract Number:  
SC0014415
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 20; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Entanglement measures; Geometric & topological phases; Quantum entanglement; Quantum error correction; Symmetry protected topological states; Topological phases of matter

Citation Formats

Schmitz, Albert T., Huang, Sheng-Jie, and Prem, Abhinav. Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter. United States: N. p., 2019. Web. doi:10.1103/physrevb.99.205109.
Schmitz, Albert T., Huang, Sheng-Jie, & Prem, Abhinav. Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter. United States. https://doi.org/10.1103/physrevb.99.205109
Schmitz, Albert T., Huang, Sheng-Jie, and Prem, Abhinav. 2019. "Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter". United States. https://doi.org/10.1103/physrevb.99.205109. https://www.osti.gov/servlets/purl/1612178.
@article{osti_1612178,
title = {Entanglement spectra of stabilizer codes: A window into gapped quantum phases of matter},
author = {Schmitz, Albert T. and Huang, Sheng-Jie and Prem, Abhinav},
abstractNote = {The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly solvable models for a plethora of gapped quantum phases of matter. Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak local perturbations thus allows us to develop a general framework within which the entanglement features of gapped topological phases can be computed and contrasted. In particular, we study models harboring fracton order, both type-I and type-II, and compare the resulting ES with that of both conventional topological order and of (strong) subsystem symmetry protected topological (SSPT) states. We find that nonlocal surface stabilizers (NLSS), a set of symmetries of the Hamiltonian which form on the boundary of the entanglement cut, act as purveyors of universal nonlocal features appearing in the entanglement spectrum. While in conventional topological orders and fracton orders, the NLSS retain a form of topological invariance with respect to the entanglement cut, subsystem symmetric systems—fracton and SSPT phases—additionally show a nontrivial geometric dependence on the entanglement cut, corresponding to the subsystem symmetry. This sheds further light on the interplay between geometric and topological effects in fracton phases of matter and demonstrates that strong SSPT phases harbour a measure of quasilocal entanglement beyond that encountered in conventional SPT phases. Here, we further show that a version of the edge-entanglement correspondence, established earlier for gapped two-dimensional topological phases, also holds for gapped three-dimensional fracton models.},
doi = {10.1103/physrevb.99.205109},
url = {https://www.osti.gov/biblio/1612178}, journal = {Physical Review. B},
issn = {2469-9950},
number = 20,
volume = 99,
place = {United States},
year = {Wed May 08 00:00:00 EDT 2019},
month = {Wed May 08 00:00:00 EDT 2019}
}

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Cited by: 14 works
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Works referencing / citing this record:

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Sorting topological stabilizer models in three dimensions
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Gauging permutation symmetries as a route to non-Abelian fractons
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