Extraction of topological information in Tomonaga-Luttinger liquids

Abstract

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 $z_L^{(q,\pm )}\equiv ⟨{\Psi }_{q/2}^{\pm }|U^q|{\Psi }_{q/2}^{\pm }⟩$, where $|{\Psi }_p^{\pm }⟩$ denotes the excited states given by linear combinations of momentum $2p{k}_{\mathrm{F}}$ with parity $\pm 1$. We found that $z_L^{(q,\pm )}$ gives universal values $\pm 1/2$ on the Tomonaga-Luttinger (TL) fixed point, and its signs identify the topology of the dominant phases. Therefore, this expectation value changes between $\pm 1/2$ discontinuously at a phase transition point with the U(1) or SU(2) symmetric Gaussian universality class. This means that $z_L^{(q,\pm )}$ 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.

9 pages, 7 figures, accepted for publication in Phys. Rev. B

References in corpus (1)

• Scaling of polarization amplitude in quantum many-body systems in one dimension

Cited by in corpus (6)

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• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Identification of gapless phases by a twisting operator
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems