Discrete symmetries and Lieb-Schultz-Mattis theorem

Abstract

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.

References in corpus (4)

• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Exact degenerate ground states for the F-AF spin chain with bond alternation
• Extension of the Lieb-Schultz-Mattis theorem
• Quantum criticality in an asymmetric three-leg spin tube: A strong rung-coupling perspective

Cited by in corpus (4)

• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Dynamical signatures of the one-dimensional deconfined quantum critical point
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point