skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on May 22, 2020

Title: Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

Abstract

Here, we study the antiferromagnetic kagome Heisenberg model with an additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of the optimization algorithm in the framework of the single-layer tensor network based on the corner transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter, and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states.

Authors:
 [1];  [2];  [1]
  1. California State Univ., Northridge, CA (United States). Dept. of Physics and Astronomy
  2. Beihang Univ., Beijing (China). Dept. of Physics
Publication Date:
Research Org.:
California State Univ., Northridge, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1515012
Alternate Identifier(s):
OSTI ID: 1515104
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 17; 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

Haghshenas, R., Gong, Shou-Shu, and Sheng, D. N. Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.174423.
Haghshenas, R., Gong, Shou-Shu, & Sheng, D. N. Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice. United States. doi:10.1103/PhysRevB.99.174423.
Haghshenas, R., Gong, Shou-Shu, and Sheng, D. N. Wed . "Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice". United States. doi:10.1103/PhysRevB.99.174423.
@article{osti_1515012,
title = {Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice},
author = {Haghshenas, R. and Gong, Shou-Shu and Sheng, D. N.},
abstractNote = {Here, we study the antiferromagnetic kagome Heisenberg model with an additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of the optimization algorithm in the framework of the single-layer tensor network based on the corner transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter, and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states.},
doi = {10.1103/PhysRevB.99.174423},
journal = {Physical Review B},
number = 17,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on May 22, 2020
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

The Quantized Hall Effect
journal, June 1983


Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states
journal, June 1990


Nature of chiral spin liquids on the kagome lattice
journal, September 2015

  • Wietek, Alexander; Sterdyniak, Antoine; Läuchli, Andreas M.
  • Physical Review B, Vol. 92, Issue 12
  • DOI: 10.1103/PhysRevB.92.125122

Tensor network study of the Shastry-Sutherland model in zero magnetic field
journal, March 2013


Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices
journal, March 2018


Projected Entangled-Pair States Can Describe Chiral Topological States
journal, December 2013


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

Topological and entanglement properties of resonating valence bond wave functions
journal, July 2012


Quantum spin liquids: a review
journal, November 2016


Finite Correlation Length Scaling with Infinite Projected Entangled-Pair States
journal, July 2018


Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model
journal, April 2014


Equivalence of the resonating-valence-bond and fractional quantum Hall states
journal, November 1987


Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet
journal, April 2011


Identifying topological order by entanglement entropy
journal, November 2012

  • Jiang, Hong-Chen; Wang, Zhenghan; Balents, Leon
  • Nature Physics, Vol. 8, Issue 12
  • DOI: 10.1038/nphys2465

Optimized contraction scheme for tensor-network states
journal, July 2017


Possible spin-liquid states on the triangular and kagomé lattices
journal, April 1993


Stripes in the two-dimensional t - J model with infinite projected entangled-pair states
journal, July 2011


Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
journal, January 2014


Chiral topological spin liquids with projected entangled pair states
journal, June 2015


Projected wave function study of Z 2 spin liquids on the kagome lattice for the spin- 1 2 quantum Heisenberg antiferromagnet
journal, July 2011


Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets
journal, September 1990


Competing States in the t - J Model: Uniform d -Wave State versus Stripe State
journal, July 2014


Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
journal, December 2018


Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet
journal, November 2015


Large- N expansion for frustrated quantum antiferromagnets
journal, April 1991


Gapless Spin-Liquid Ground State in the S = 1 / 2 Kagome Antiferromagnet
journal, March 2017


Unifying projected entangled pair state contractions
journal, March 2014


Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
journal, November 2014


Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
journal, October 2014

  • Bauer, B.; Cincio, L.; Keller, B. P.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms6137

Spin Dynamics of the Spin- 1 / 2 Kagome Lattice Antiferromagnet ZnCu 3 ( OH ) 6 Cl 2
journal, March 2007


Gapless boundary excitations in the quantum Hall states and in the chiral spin states
journal, May 1991


Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
journal, October 2010


Spin liquids in frustrated magnets
journal, March 2010


Anyons in an exactly solved model and beyond
journal, January 2006


Theory of the edge States in Fractional Quantum hall Effects
journal, May 1992


Chiral Projected Entangled-Pair State with Topological Order
journal, March 2015


Chiral spin states and superconductivity
journal, June 1989


Dirac structure, RVB, and Goldstone modes in the kagomé antiferromagnet
journal, December 2000


Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
journal, April 1989


Projected-Wave-Function Study of the Spin- 1 / 2 Heisenberg Model on the Kagomé Lattice
journal, March 2007


Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
journal, November 2018


Gapless spin-liquid phase in the kagome spin- 1 2 Heisenberg antiferromagnet
journal, February 2013


Ground state of the spin-1/2 kagome-lattice Heisenberg antiferromagnet
journal, November 2007


Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model
journal, November 1997


String-net condensation: A physical mechanism for topological phases
journal, January 2005


Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
journal, March 2012


Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states
journal, September 2017


Resonating valence bonds: A new kind of insulator?
journal, February 1973


Accurate computation of low-temperature thermodynamics for quantum spin chains
journal, December 2012


Quantized Hall conductivity in two dimensions
journal, May 1981


Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states
journal, April 2010


Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008


Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model
journal, July 2017


Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing
journal, July 2015


Nature of the Spin-Liquid Ground State of the S = 1 / 2 Heisenberg Model on the Kagome Lattice
journal, August 2012


Uni10: an open-source library for tensor network algorithms
journal, September 2015


Resonating valence bond states in the PEPS formalism
journal, September 2012