DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nature of Continuous Phase Transitions in Interacting Topological Insulators

Abstract

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [2];  [1]
  1. California State Univ. (CalState), Northridge, CA (United States). Dept. of Physics and Astronomy
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
OSTI Identifier:
1416285
Alternate Identifier(s):
OSTI ID: 1408066
Report Number(s):
LA-UR-17-26330
Journal ID: ISSN 2469-9950; TRN: US1800897
Grant/Contract Number:  
AC52-06NA25396; DMR-1205734; DMR-1408560
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Material Science; Antiferromagnetism; Quantum spin Hall effect

Citation Formats

Zeng, Tian-sheng, Zhu, Wei, Zhu, Jianxin, and Sheng, Donna N. Nature of Continuous Phase Transitions in Interacting Topological Insulators. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.195118.
Zeng, Tian-sheng, Zhu, Wei, Zhu, Jianxin, & Sheng, Donna N. Nature of Continuous Phase Transitions in Interacting Topological Insulators. United States. https://doi.org/10.1103/PhysRevB.96.195118
Zeng, Tian-sheng, Zhu, Wei, Zhu, Jianxin, and Sheng, Donna N. Wed . "Nature of Continuous Phase Transitions in Interacting Topological Insulators". United States. https://doi.org/10.1103/PhysRevB.96.195118. https://www.osti.gov/servlets/purl/1416285.
@article{osti_1416285,
title = {Nature of Continuous Phase Transitions in Interacting Topological Insulators},
author = {Zeng, Tian-sheng and Zhu, Wei and Zhu, Jianxin and Sheng, Donna N.},
abstractNote = {Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.},
doi = {10.1103/PhysRevB.96.195118},
journal = {Physical Review B},
number = 19,
volume = 96,
place = {United States},
year = {Wed Nov 08 00:00:00 EST 2017},
month = {Wed Nov 08 00:00:00 EST 2017}
}

Journal Article:

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Stability of the quantum spin Hall effect: Effects of interactions, disorder, and Z 2 topology
journal, January 2006


Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
journal, January 2015


Exotic continuous quantum phase transition between Z 2 topological spin liquid and Néel order
journal, December 2012


Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
journal, September 2014

  • Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
  • Scientific Reports, Vol. 4, Issue 1
  • DOI: 10.1038/srep06317

Antiferromagnetic topological insulator state in the correlated Bernevig-Hughes-Zhang model
journal, May 2013


Mott physics and band topology in materials with strong spin–orbit interaction
journal, March 2010

  • Pesin, Dmytro; Balents, Leon
  • Nature Physics, Vol. 6, Issue 5
  • DOI: 10.1038/nphys1606

Geometric Phases and Criticality in Spin-Chain Systems
journal, October 2005


Rashba spin-orbit coupling in the Kane-Mele-Hubbard model
journal, October 2014


Phase diagram of the Kane-Mele-Coulomb model
journal, August 2014


Universality class of the Mott transition in two dimensions
journal, October 2012


Scaling of Geometric Phases Close to the Quantum Phase Transition in the X Y Spin Chain
journal, February 2006


Anisotropic quantum spin Hall effect, spin-orbital textures, and the Mott transition
journal, December 2013


Quantum topological phase transition at the microscopic level
journal, February 2008


Detecting Topological Order through a Continuous Quantum Phase Transition
journal, January 2006


Transition from the Z 2 spin liquid to antiferromagnetic order: Spectrum on the torus
journal, August 2016


Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
journal, August 2013


Correlation effects in two-dimensional topological insulators
journal, March 2013


Phase diagram of the spin- 1 2 J 1 - J 2 Heisenberg model on a honeycomb lattice
journal, October 2013


Phase Diagram for Quantum Hall Bilayers at ν = 1
journal, September 2003


Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
journal, June 2014


Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator
journal, January 2012


Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
journal, February 2013


Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
journal, March 2011


Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
journal, November 2011


Nearly Flatbands with Nontrivial Topology
journal, June 2011


Nondissipative Spin Hall Effect via Quantized Edge Transport
journal, September 2005


Continuous and discontinuous topological quantum phase transitions
journal, July 2016


Phase diagram of the Kane-Mele-Hubbard model
journal, January 2012


Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order
journal, April 2008


Detection and characterization of symmetry-broken long-range orders in the spin- 1 2 triangular Heisenberg model
journal, August 2017


Z2 Topological Order and the Quantum Spin Hall Effect
journal, September 2005


Quantum Spin Hall Effect in Graphene
journal, November 2005


Flux insertion, entanglement, and quantized responses
journal, October 2014

  • Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 10
  • DOI: 10.1088/1742-5468/2014/10/P10007

Topological Orders in Rigid States
journal, February 1990


Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
journal, June 2011


Fidelity Approach to Quantum Phase Transitions
journal, September 2010


Critical phenomena and renormalization-group theory
journal, October 2002


Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
journal, September 2011


Topological insulators and Mott physics from the Hubbard interaction
journal, August 2010


Phase diagram of the strongly correlated Kane-Mele-Hubbard model
journal, May 2012


Correlation effects on a topological insulator at finite temperatures
journal, March 2012


Topological Phase Transitions in the Repulsively Interacting Haldane-Hubbard Model
journal, June 2016


Quantum phase transitions in the Kane-Mele-Hubbard model
journal, March 2012


Two-component quantum Hall effects in topological flat bands
journal, March 2017


Bosonic integer quantum Hall effect as topological pumping
journal, April 2017


Fluctuation-induced topological quantum phase transitions in quantum spin-Hall and anomalous-Hall insulators
journal, November 2012


Quantum Spin-Hall Effect and Topologically Invariant Chern Numbers
journal, July 2006


Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- 1 2 J 1 J 2 Square Heisenberg Model
journal, July 2014


Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase
journal, October 2015

  • Samkharadze, N.; Schreiber, K. A.; Gardner, G. C.
  • Nature Physics, Vol. 12, Issue 2
  • DOI: 10.1038/nphys3523

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
journal, January 2009


Magnetic ordering phenomena of interacting quantum spin Hall models
journal, October 2012


Quantum Spin Hall Effect in a Transition Metal Oxide Na 2 IrO 3
journal, June 2009


First-Order Character and Observable Signatures of Topological Quantum Phase Transitions
journal, May 2015


Z 2 topological invariants in two dimensions from quantum Monte Carlo
journal, May 2013


Quantum spin Hall insulators with interactions and lattice anisotropy
journal, May 2012


Effects of Interaction on Quantum Spin Hall Insulators
journal, October 2011


Topological phase transitions for interacting finite systems
journal, December 2011


Works referencing / citing this record:

Interacting topological insulators: a review
journal, October 2018


Determining topological order from infinite projected entangled pair states
journal, January 2020


Interacting topological insulators: a review
text, January 2018


Determining topological order from infinite projected entangled pair states
text, January 2019