Phase diagrams of spin-$S$ Kitaev ladders

TL;DR

This paper explores the ground states of spin-$S$ Kitaev ladders, revealing an even-odd effect where half-integer spins exhibit SSB and SPT phases, while integer spins show SSB and trivial paramagnetic phases, with detailed phase transition analysis.

Contribution

It provides the first comprehensive analysis of phase diagrams of spin-$S$ Kitaev ladders, highlighting the even-odd effect and characterizing phase transitions using multiple methods.

Findings

Half-integer $S$ ladders have SSB and SPT phases.

Integer $S$ ladders have SSB and trivial paramagnetic phases.

Distinct phase transitions occur between SPT orders for half-integer $S$.

Abstract

We investigate the ground states of spin-$S$ Kitaev ladders using exact analytical solutions (for $S = 1/2$), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer $S$, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer $S$, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer $S$ we find a transition between two distinct SPT orders, and for integer $S$ we find unnecessary first order phase transitions within a trivial phase