arXiv subjects

Takaichi Isoyama

Publications and source records attributed to Takaichi Isoyama.

2 recordsLinked to original sources

arXiv2017

Discrete symmetries and Lieb-Schultz-Mattis theorem

In this study, we consider one-dimension (1D) quantum spin systems with the 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 theorem \cite{Lieb-Schultz-Mattis-1961}\cite{Nomura-Morishige-Isoyama-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 the discrete symmetries.

cond-mat.stat-mech↗

arXiv2015

Extension of the Lieb-Schultz-Mattis theorem

Lieb, Schultz and Mattis (LSM) studied the S=1/2 XXZ spin chain. Theorems of LSM's paper can be applied to broader models. In the original LSM theorem it was assumed the nonfrustrating system. However, reconsidering the LSM theorem, we can extend the LSM theorem for frustrating systems. Next, several researchers have tried to extend the LSM theorem for excited states. In the cases $S^{z}_{T} = \pm 1,\pm 2 \cdots$, the lowest energy eigenvalues are continuous for wave number $q$. But we find that their proofs are insufficient, and we improve them. In addition, we can prove the LSM theory without the assumption of the discrete symmetry, which means that the LSM type theorems are applicable for Dzyaloshinskii-Moriya type interactions or other nonsymmetric models.

cond-mat.stat-mech↗