Topological phases in two-legged Heisenberg ladders with alternating interactions

TL;DR

This paper investigates topological phases in two-legged Heisenberg ladders with staggered interactions, revealing a critical point and characterizing two distinct phases as Mott and Haldane insulators through numerical analysis.

Contribution

It introduces a model with staggered interactions in spin ladders, maps it to a non-linear sigma model with a topological term, and characterizes the resulting phases numerically.

Findings

Identification of a critical point separating two phases.

Characterization of one phase as a Mott insulator.

Characterization of the other phase as a Haldane insulator.

Abstract

We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$\sigma$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.