Phase diagram of the Z3 parafermionic chain with chiral interactions
Abstract
Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in one-dimensional models that are generalizations of the Kitaev p-wave wire. Here, we study the simplest generalization, i.e., the Z3 parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.
- Authors:
-
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF)
- OSTI Identifier:
- 1565366
- Alternate Identifier(s):
- OSTI ID: 1206813
- Grant/Contract Number:
- AC05-00OR22725; SC0008692; NA0001789; FG02-12ER46875; OCI-1053575; DMR 1351895-CAR
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 3; Journal ID: ISSN 1098-0121
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Zhuang, Ye, Changlani, Hitesh J., Tubman, Norm M., and Hughes, Taylor L. Phase diagram of the Z3 parafermionic chain with chiral interactions. United States: N. p., 2015.
Web. doi:10.1103/physrevb.92.035154.
Zhuang, Ye, Changlani, Hitesh J., Tubman, Norm M., & Hughes, Taylor L. Phase diagram of the Z3 parafermionic chain with chiral interactions. United States. https://doi.org/10.1103/physrevb.92.035154
Zhuang, Ye, Changlani, Hitesh J., Tubman, Norm M., and Hughes, Taylor L. Fri .
"Phase diagram of the Z3 parafermionic chain with chiral interactions". United States. https://doi.org/10.1103/physrevb.92.035154. https://www.osti.gov/servlets/purl/1565366.
@article{osti_1565366,
title = {Phase diagram of the Z3 parafermionic chain with chiral interactions},
author = {Zhuang, Ye and Changlani, Hitesh J. and Tubman, Norm M. and Hughes, Taylor L.},
abstractNote = {Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in one-dimensional models that are generalizations of the Kitaev p-wave wire. Here, we study the simplest generalization, i.e., the Z3 parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.},
doi = {10.1103/physrevb.92.035154},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 3,
volume = 92,
place = {United States},
year = {Fri Jul 31 00:00:00 EDT 2015},
month = {Fri Jul 31 00:00:00 EDT 2015}
}
Web of Science
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