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Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks.

Hyun-Yong Lee1, Ryui Kaneko1, Tsuyoshi Okubo2

  • 1Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.

Physical Review Letters
|September 7, 2019
PubMed
Summary

We introduce a tensor network (TN) framework to explain the Kitaev spin liquid (KSL). This approach reveals a hidden string gas structure and accurately models KSL properties without Majorana fermions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism

Background:

  • The Kitaev spin liquid (KSL) is a fascinating quantum state of matter with exotic properties.
  • Understanding the KSL's complex features, such as its gauge structure and criticality, remains a challenge.
  • Traditional approaches often rely on Majorana fermions, complicating theoretical descriptions.

Purpose of the Study:

  • To develop a novel framework for understanding the gapless Kitaev spin liquid (KSL).
  • To explain KSL properties using tensor network (TN) representations.
  • To reveal the underlying structure of the KSL without invoking Majorana fermions.

Main Methods:

  • Development of a tensor network (TN) framework.
  • Compact TN representation of the gapless KSL.
  • Analysis of symmetries, gauge structure, criticality, and vortex properties within the TN language.
  • Identification of a hidden string gas structure.

Main Results:

  • A compact TN representation accurately captures key KSL features.
  • The framework explains KSL properties without requiring Majorana fermions.
  • A hidden string gas structure within the KSL is revealed.
  • An accurate KSL Ansatz was obtained with minimal variational parameters (two) and bond dimension D=8.
  • The calculated energy is remarkably close to the exact value (0.007% higher).

Conclusions:

  • Tensor network provides a powerful and intuitive language for understanding Kitaev spin liquids.
  • The TN framework offers a simplified yet accurate description of KSL, highlighting its string gas nature.
  • This work paves the way for further exploration of topological phases of matter using TN methods.