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Title: (2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

Abstract

The (2+1)-dimensional continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground-state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground-state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. Here, these are two different U(1) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton and lineon-elasticity dualities for the Lifshitz theory, and scalar and vector charge gauge theories.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3];  [4]
+ Show Author Affiliations
  1. Princeton University, NJ (United States)
  2. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
  3. Institute for Advanced Study, Princeton, NJ (United States)
  4. Stony Brook University, NY (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE; Simons Foundation; National Science Foundation (NSF)
OSTI Identifier:
1998176
Alternate Identifier(s):
OSTI ID: 2222881
Grant/Contract Number:  
SC0009988; 651440; PHY-2210182
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 108; Journal Issue: 7; 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; Exotic phases of matter; Lattice dynamics; XY model; 2-dimensional systems; Lattice types; Quantum many-body systems; Strongly correlated systems; Duality; Exact solutions for many-body systems; Field & string theory models & techniques; Lattice models in condensed matter; Quantum field theory; Symmetries; Symmetries in condensed matter

Citation Formats

Gorantla, Pranay, Lam, Ho Tat, Seiberg, Nathan, and Shao, Shu-Heng. (2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons. United States: N. p., 2023. Web. doi:10.1103/physrevb.108.075106.
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Gorantla, Pranay, Lam, Ho Tat, Seiberg, Nathan, & Shao, Shu-Heng. (2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons. United States. https://doi.org/10.1103/physrevb.108.075106
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Gorantla, Pranay, Lam, Ho Tat, Seiberg, Nathan, and Shao, Shu-Heng. Thu . "(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons". United States. https://doi.org/10.1103/physrevb.108.075106.
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@article{osti_1998176,
title = {(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons},
author = {Gorantla, Pranay and Lam, Ho Tat and Seiberg, Nathan and Shao, Shu-Heng},
abstractNote = {The (2+1)-dimensional continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground-state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground-state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. Here, these are two different U(1) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton and lineon-elasticity dualities for the Lifshitz theory, and scalar and vector charge gauge theories.},
doi = {10.1103/physrevb.108.075106},
journal = {Physical Review. B},
number = 7,
volume = 108,
place = {United States},
year = {Thu Aug 03 00:00:00 EDT 2023},
month = {Thu Aug 03 00:00:00 EDT 2023}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/physrevb.108.075106
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