Discrete symmetries and the Lieb-Schultz-Mattis theorem

Takaichi Isoyama, Kiyohide Nomura

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4 Citations (Scopus)


In this study, we consider one-dimensional (1D) quantum spin systems with translation and discrete symmetries (spin reversal, space inversion, and time reversal symmetries). By combining the continuous U(1) symmetry with the discrete symmetries and using the extended Lieb-Schultz-Mattis (LSM) theorem [E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 16, 407 (1961); K. Nomura, J. Morishige, and T. Isoyama, J. Phys. A 48, 375001 (2015)], we investigate the relation between the ground states, energy spectra, and symmetries. For half-integer spin cases, we generalize the dimer and Néel concepts using the discrete symmetries, and we can reconcile the LSM theorem with the dimer or Néel states, since there was a subtle dilemma. Furthermore, a part of discrete symmetries is enough to classify possible phases. Thus we can deepen our understanding of the relation between the LSM theorem and discrete symmetries.

Original languageEnglish
Article number103I01
JournalProgress of Theoretical and Experimental Physics
Issue number10
Publication statusPublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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