Finitely Correlated Generalized Spin Ladders

TL;DR

This paper provides exact solutions for two families of generalized spin ladder models, revealing phase boundaries, elementary excitations, and a rich phase diagram with potential applications in understanding quantum phase transitions.

Contribution

It introduces two new families of exactly solvable spin ladder models, including models with translational invariance and spontaneous dimerization, and analyzes their phase transitions and excitations.

Findings

Exact phase boundary for dimerized phase determined.

Elementary excitations become gapless at second-order transitions.

Rich phase diagram with exact phase boundaries.

Abstract

We study two-leg S=1/2 ladders with general isotropic exchange interactions between spins on neighboring rungs, whose ground state can be found exactly in a form of finitely correlated (matrix product) wave function. Two families of models admitting an exact solution are found: one yields translationally invariant ground states and the other describes spontaneously dimerized models with twofold degenerate ground state. Several known models with exact ground states can be obtained as particular cases from the general solution of the first family, which includes also a set of models with only bilinear interactions. Those two families of models have nonzero intersection, which enables us to determine exactly the phase boundary of the second-order transition into the dimerized phase and to study the properties of this transition. The structure of elementary excitations in the dimerized phase is discussed on the basis of a variational ansatz. For a particular class of models, we present exact wave functions of the elementary excitations becoming gapless at second-order transition lines. We also propose a generalization of the Bose-Gayen ladder model which has a rich phase diagram with all phase boundaries being exact.