Extraction of topological information in Tomonaga-Luttinger liquids

Masaaki Nakamura and Shunsuke C. Furuya
Phys. Rev. B 99, 075128 – Published 13 February 2019

Abstract

We discuss expectation values of the twist operator U appearing in the Lieb-Schultz-Mattis theorem (or the polarization operator for periodic systems) in excited states of the one-dimensional correlated systems zL(q,±)Ψq/2±|Uq|Ψq/2±, where |Ψp± denotes the excited states given by linear combinations of momentum 2pkF with parity ±1. We found that zL(q,±) gives universal values ±1/2 on the Tomonaga-Luttinger (TL) fixed point, and its signs identify the topology of the dominant phases. Therefore, this expectation value changes between ±1/2 discontinuously at a phase transition point with the U(1) or SU(2) symmetric Gaussian universality class. This means that zL(q,±) extracts the topological information of TL liquids. We explain these results based on the free-fermion picture and the bosonization theory, and also demonstrate them in several physical systems.

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  • Received 22 June 2018
  • Revised 24 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.075128

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Masaaki Nakamura1 and Shunsuke C. Furuya2

  • 1Department of Physics, Ehime University Bunkyo-cho 2-5, Matsuyama, Ehime 790-8577, Japan
  • 2Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

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Issue

Vol. 99, Iss. 7 — 15 February 2019

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