Energy-level ordering and ground-state quantum numbers for frustrated two-leg spin-1/2 ladder model

TL;DR

This paper extends the Lieb-Mattis theorem to a frustrated two-leg spin-1/2 ladder model, proving energy level ordering, ground state uniqueness, and quantum numbers for various coupling regimes.

Contribution

It provides the first exact proofs of energy level ordering and ground state properties for a frustrated ladder model with site-dependent interactions.

Findings

Lowest energy levels increase with total spin.

Ground state is a unique spin singlet for many couplings.

Results apply to models with boundary impurities and partial periodic conditions.

Abstract

The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels on bipartite lattices is generalized to finite-size two-leg spin-1/2 ladder model frustrated by diagonal interactions. For reflection-symmetric model with site-dependent interactions we prove exactly that the lowest energies in sectors with fixed total spin and reflection quantum numbers are monotone increasing functions of total spin. The nondegeneracy of most levels is proved also. We also establish the uniqueness and obtain the spin value of the lowest-level multiplet in the whole sector formed by reflection-symmetric (antisymmetric) states. For a wide range of coupling constants, we prove that the ground state is a unique spin singlet. For other values of couplings, it may be also a unique spin triplet or may consist of both multiplets. Similar results have been obtained for the ladder with arbitrary boundary impurity spin. Some partial results have also been obtained in the case of periodical boundary conditions.