A new family of models with exact ground states connecting smoothly the S=1/2 dimer and S=1 Haldane phases of 1D spin chains

TL;DR

This paper introduces a family of exactly solvable 1D spin chain models that smoothly connect the S=1/2 dimer and S=1 Haldane phases, revealing they belong to the same phase and expanding understanding of quantum phase transitions.

Contribution

The authors present new models with exact ground states that interpolate between different quantum phases, demonstrating phase continuity and providing exactly solvable examples of frustrated spin chains.

Findings

Models connect S=1/2 dimer and S=1 Haldane phases smoothly.

Ground states can be exactly determined using matrix product wavefunctions.

Models include frustrated spin chains with only bilinear interactions.

Abstract

We investigate the isotropic two-leg S=1/2 ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians which have a matrix product wavefunction as exact ground state. We demonstrate that a smooth change of parameters leads one from the S=1/2 dimer and Majumdar-Ghosh chains to the S=1 chain with biquadratic exchange. This proves that these model systems are in the same phase. We also present a new set of models of frustrated S=1/2 spin chains (including only bilinear NN and NNN interactions) whose ground states can be found exactly.