On the valence-bond solid phase of the crossed-chain quantum spin model

TL;DR

This study investigates the valence-bond solid phase in a crossed-chain quantum spin model using series expansion, revealing the effects of frustration on triplet excitations, phase transitions, and the stability of the ground state.

Contribution

It introduces a flow-equation based series expansion approach to analyze the ground state and excitations of a generalized crossed spin-1/2 chain model, highlighting frustration effects.

Findings

Triplet dispersion is highly sensitive to inter-quadrumer frustration.

A finite spin-gap exists near the checkerboard point, consistent with exact diagonalization.

The ground state energy is lower than the quadrumer case across studied couplings.

Abstract

Using a series expansion based on the flow-equation method we study the ground state energy and the elementary triplet excitations of a generalized model of crossed spin-1/2 chains starting from the limit of decoupled quadrumers. The triplet dispersion is shown to be very sensitive to the inter-quadrumer frustration, exhibiting a line of almost complete localization as well as lines of quantum phase transitions limiting the stability of the valence-bond solid phase. In the vicinity of the checkerboard-point a finite window of exchange couplings is found with a non-zero spin-gap, consistent with known results from exact diagonalization. The ground state energy is lower than that of the bare quadrumer case for all exchange couplings investigated. In the limiting situation of the fully frustrated checkerboard magnet our results agree with earlier series expansion studies.