Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection

TL;DR

This paper develops an effective field theory for one-dimensional valence-bond-solid phases, revealing how certain symmetries protect phase distinctions and predicting a new symmetry that separates trivial phases.

Contribution

The paper introduces a novel effective field theory approach that identifies a previously unrecognized symmetry protecting VBS phases and applies it to phase transitions and generalized Lieb-Schultz-Mattis theorems.

Findings

Identifies a new symmetry combining site-centered inversion and spin rotation.

Demonstrates that this symmetry distinguishes trivial phases beyond entanglement.

Provides applications to phase transitions and non-translational-invariant systems.

Abstract

We investigate valence-bond-solid (VBS) phases in one-dimensional spin systems by an effective field theory developed by Schulz [Phys. Rev. B 34, 6372 (1986)]. While the distinction among the VBS phases are often understood in terms of different entanglement structures protected by certain symmetries, we adopt a different but more fundamental point of view, that is, different VBS phases are separated by a gap closing under certain symmetries. In this way, the effective field theory reproduces the known three symmetries: time reversal, bond-centered inversion, and dihedral group of spin rotations. It also predicts that there exists another symmetry: site-centered inversion combined with a spin rotation by $\pi$. We demonstrate that the last symmetry gives distinct trivial phases, which cannot be characterized by their entanglement structure, in terms of a simple perturbative analysis in a spin chain. We also discuss several applications of the effective field theory to the phase transitions among VBS phases in microscopic models and an extension of the Lieb-Schultz-Mattis theorem to non-translational-invariant systems.