Abstract
We discuss expectation values of the twist operator appearing in the Lieb-Schultz-Mattis theorem (or the polarization operator for periodic systems) in excited states of the one-dimensional correlated systems , where denotes the excited states given by linear combinations of momentum with parity . We found that gives universal values on the Tomonaga-Luttinger (TL) fixed point, and its signs identify the topology of the dominant phases. Therefore, this expectation value changes between discontinuously at a phase transition point with the U(1) or SU(2) symmetric Gaussian universality class. This means that extracts the topological information of TL liquids. We explain these results based on the free-fermion picture and the bosonization theory, and also demonstrate them in several physical systems.
- Received 22 June 2018
- Revised 24 December 2018
DOI:https://doi.org/10.1103/PhysRevB.99.075128
©2019 American Physical Society