Unconventional quantum phase transitions in a one-dimensional Lieb-Schultz-Mattis system

TL;DR

This paper investigates unconventional quantum phase transitions in a one-dimensional fermionic system with a Lieb-Schultz-Mattis anomaly, revealing novel critical behaviors and phases beyond traditional theories.

Contribution

It proves a Lieb-Schultz-Mattis theorem for the system, identifies a 1D deconfined quantum critical point described by Tomonaga-Luttinger liquid theory, and uncovers a gapless phase beyond standard models.

Findings

Gapped ground states must be Kitaev chains or break symmetry.

Continuous phase transitions beyond Ginzburg-Landau-Wilson paradigm.

Identification of a non-U(1) gapless phase.

Abstract

We study quantum phases and phase transitions in a one-dimensional interacting fermion system with a Lieb-Schultz-Mattis (LSM) type anomaly. Specifically, the inversion symmetry enforces any symmetry-preserving gapped ground state of the system to be a Kitaev chain, following a Lieb-Schultz-Mattis type theorem that we prove. Alternatively, via the Jordan-Wigner transformation, this system describes a spin system whose gapped ground states must break either the inversion or the Ising symmetry associated with fermion parity. We obtain a phase diagram using analytical methods and variational matrix product state simulations, and study the critical behaviors of the quantum phase transitions therein using entanglement entropy, energy variance and finite size scaling of order parameters. In particular, we observe continuous phase transitions between different ordered phases that are beyond the Ginzburg-Landau-Wilson paradigm, in analogy to the deconfined quantum critical points in two spatial dimensions. We show this type of 1D deconfined quantum critical point is described by the Tomonaga-Luttinger liquid theory, and extract the Luttinger parameter and critical exponents. We also identify a gapless phase between two ordered phases, which cannot be described by a U(1) Luttinger liquid.