Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

TL;DR

This paper investigates a quantum spin ladder with long-range interactions, revealing a continuous transition from a non-local string ordered phase to a magnetically ordered phase, with detailed spectral analysis and implications for deconfined criticality.

Contribution

It demonstrates a second-order quantum phase transition in a long-range interacting spin ladder, combining QMC and DMRG methods to analyze spectral properties and critical behavior.

Findings

Transition from string order to Ne9el order is second order.

Gapless modes in the ordered phase and triplon excitations in the gapped phase.

Evolution of triplon band into gapless magnon dispersion at the transition.

Abstract

We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $\alpha$. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N\'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.