Phase diagram and hidden order for generalized spin ladders

TL;DR

This paper explores the phase diagram of generalized antiferromagnetic spin ladders with additional interactions, revealing hidden order and phase relationships through variational and numerical methods.

Contribution

It introduces a unified analysis of various spin ladder models and demonstrates the presence of hidden order similar to the antiferromagnetic S=1 chain using matrix product states.

Findings

Majumdar-Ghosh states exhibit hidden order akin to S=1 chains

Ground state energies align with variational calculations

Dimer and Majumdar-Ghosh points share the same phase as antiferromagnetic S=1 chain

Abstract

We investigate the phase diagram of antiferromagnetic spin ladders with additional exchange interactions on diagonal bonds by variational and numerical methods. These generalized spin ladders interpolate smoothly between the $S=1/2$ chain with competing nn and nnn interactions, the $S=1/2$ chain with alternating exchange and the antiferromagnetic $S=1$ chain. The Majumdar-Ghosh ground states are formulated as matrix product states and are shown to exhibit the same type of hidden order as the af $S=1$ chain. Generalized matrix product states are used for a variational calculation of the ground state energy and the spin and string correlation functions. Numerical (Lanczos) calculations of the energies of the ground state and of the low-lying excited states are performed, and compare reasonably with the variational approach. Our results support the hypothesis that the dimer and Majumdar-Ghosh points are in the same phase as the af $S=1$ chain.