Soluble limit and criticality of fermions in $$\mathbb Z_2$$ gauge theories
Abstract
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$$T_c$$ systems), entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, in this paper we introduce a simple model for fermions moving in the deconfined phase of a $$\mathbb Z_2$$ gauge theory by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code permits us to tune the ground state between an orthogonal metal and an orthogonal semimetal in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a diagrammatic technique, we are able to explore physics beyond the integrable point to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit, thus providing an important link between quantum materials and quantum information theory.
- Authors:
-
[1];
[3]
- Rutgers Univ., Piscataway, NJ (United States)
- Rutgers Univ., Piscataway, NJ (United States); Univ. of London, Surrey (United Kingdom)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1668654
- Report Number(s):
- BNL-219878-2020-JAAM
Journal ID: ISSN 2469-9950; TRN: US2203709
- Grant/Contract Number:
- SC0012704; FG02-99ER45790
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 15; 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
Citation Formats
Konig, Elio J., Coleman, Piers, and Tsvelik, Alexei M. Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories. United States: N. p., 2020.
Web. doi:10.1103/PhysRevB.102.155143.
Konig, Elio J., Coleman, Piers, & Tsvelik, Alexei M. Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories. United States. https://doi.org/10.1103/PhysRevB.102.155143
Konig, Elio J., Coleman, Piers, and Tsvelik, Alexei M. Tue .
"Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories". United States. https://doi.org/10.1103/PhysRevB.102.155143. https://www.osti.gov/servlets/purl/1668654.
@article{osti_1668654,
title = {Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories},
author = {Konig, Elio J. and Coleman, Piers and Tsvelik, Alexei M.},
abstractNote = {Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems), entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, in this paper we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code permits us to tune the ground state between an orthogonal metal and an orthogonal semimetal in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a diagrammatic technique, we are able to explore physics beyond the integrable point to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit, thus providing an important link between quantum materials and quantum information theory.},
doi = {10.1103/PhysRevB.102.155143},
journal = {Physical Review B},
number = 15,
volume = 102,
place = {United States},
year = {Tue Oct 27 00:00:00 EDT 2020},
month = {Tue Oct 27 00:00:00 EDT 2020}
}
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