Extraction of topological information in Tomonaga-Luttinger liquids

Article

关键词: MECHANICAL POSITION-OPERATOR;    BOND GROUND-STATES;    SPIN CHAINS;    QUANTUM;    LOCALIZATION;    MODEL;    GAP;   

DOI  :  10.1103/PhysRevB.99.075128

来源: SCIE

【 摘 要 】

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 Z(L)((q,+/-)) , where vertical bar Psi(+/-)(p)> denotes the excited states given by linear combinations of momentum 2pk(F) with parity +/- 1. We found that Z(L)((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 Z(L)((q,)(+/-)) extracts the topological information of TL liquids. We explain these results based on the freefermion picture and the bosonization theory, and also demonstrate them in several physical systems.

【 授权许可】

Free