TY - JOUR

T1 - Discrete symmetries and the Lieb-Schultz-Mattis theorem

AU - Isoyama, Takaichi

AU - Nomura, Kiyohide

N1 - Publisher Copyright:
© The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063079939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063079939&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptx139

DO - 10.1093/ptep/ptx139

M3 - Article

AN - SCOPUS:85063079939

SN - 2050-3911

VL - 2017

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

IS - 10

M1 - 103I01

ER -