Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction

TL;DR

This paper explores a spin-1/2 XXZ ladder model with four-spin interactions, revealing a rich phase diagram with eight gapped phases, including symmetry-breaking and featureless topological phases, and characterizing their phase transitions.

Contribution

It introduces a comprehensive analysis of the phase diagram of a spin-1/2 XXZ ladder with four-spin interactions, identifying new topological and symmetry-breaking phases and their critical behaviors.

Findings

Eight distinct gapped phases identified.

Topological phases distinguished by symmetry-based indices.

Gaussian and Ising transitions characterize phase boundaries.

Abstract

We study a spin-1/2 XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairs are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge c=1 occur between the featureless phases and between the ordered phases while Ising transitions with c=1/2 occur between the featureless and ordered phases. The two types of transition lines cross at the SU(2)-symmetric point, where the criticality is described by the SU(2)_2 Wess-Zumino-Witten theory with c=3/2. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.