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Title: Phase diagram of the Z3 parafermionic chain with chiral interactions

Journal Article · · Physical Review. B, Condensed Matter and Materials Physics
 [1];  [1];  [1];  [1]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
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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.

Research Organization:
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 Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF)
Grant/Contract Number:
AC05-00OR22725; SC0008692; NA0001789; FG02-12ER46875; OCI-1053575; DMR 1351895-CAR
OSTI ID:
1565366
Alternate ID(s):
OSTI ID: 1206813
Journal Information:
Physical Review. B, Condensed Matter and Materials Physics, Vol. 92, Issue 3; ISSN 1098-0121
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 44 works
Citation information provided by
Web of Science

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Fock Parafermions and Self-Dual Representations of the Braid Group text January 2013
Parafermions in Interacting Nanowire Bundle text January 2013
Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators text January 2014
Stability of zero modes in parafermion chains text January 2014
Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models text January 2014

Cited By (18)

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator journal April 2019
Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model journal April 2018
Topological phase, supercritical point, and emergent phenomena in an extended parafermion chain journal September 2019
Energy transport in an integrable parafermionic chain via generalized hydrodynamics journal August 2018
Decoding quantum criticality from fermionic/parafermionic topological states journal October 2018
Exact results for a Z 3 -clock-type model and some close relatives journal December 2018
Nonequilibrium critical dynamics in the quantum chiral clock model journal May 2019
Tunable Splitting of the Ground-State Degeneracy in Quasi-One-Dimensional Parafermion Systems journal March 2016
Parafermionic Wires at the Interface of Chiral Topological States journal March 2017
Topological Phases of Parafermions: A Model with Exactly Solvable Ground States journal April 2017
Parafermionic phases with symmetry-breaking and topological order text January 2015
Topological phases of parafermions: a model with exactly-solvable ground states text January 2016
Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing text January 2018
Decoding quantum criticalities from fermionic/parafermionic topological states text January 2018
Energy transport in an integrable parafermionic chain via generalized hydrodynamics text January 2018
Floquet time crystals in clock models text January 2018
Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models text January 2019
Laughlin-like states in bosonic and fermionic atomic synthetic ladders text January 2016

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