Quantum phase transitions in three-leg spin tubes

TL;DR

This paper explores the complex phase diagram of a three-leg quantum spin tube with integer spins, revealing multiple phase transitions and the nature of these transitions using various theoretical and numerical methods.

Contribution

It introduces a detailed analysis of phase transitions in three-leg spin tubes, highlighting the role of hidden symmetries and string order parameters, especially for S=1.

Findings

Identification of 2S phase transitions for integer spins.

Existence of two Haldane phases separated by a trivial state.

Evidence of a first order transition near a tricritical point.

Abstract

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density matrix renormalization group method, strong coupling approaches and the non linear sigma model. For integer spins S, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S phase transitions. They can be accurately identified by the behavior of a non local string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions are further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S = 1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first order phase transition but at the close proximity of a tricritical point separating a gapless and a first order transition line in the phase diagram of the quantum spin tube.