Mean-Field Theory for Spin Ladders Using Angular-Momentum Coupled Bases

TL;DR

This paper develops a generalized mean-field approach using angular-momentum coupled bases to better understand the properties of two-leg Heisenberg spin ladders, improving the accuracy of static and dynamic property calculations.

Contribution

It extends the mean-field theory for spin ladders to larger angular-momentum bases, capturing more short-range correlations and reducing quasiparticle coupling.

Findings

Ground-state condensate fraction increases with basis size

Weak-coupling approximation becomes more accurate with larger bases

Method effectively computes static and dynamic properties

Abstract

We study properties of two-leg Heisenberg spin ladders in a mean-field approximation using a variety of angular-momentum coupled bases. The mean-field theory proposed by Gopalan, Rice, and Sigrist, which uses a rung basis, assumes that the mean-field ground state consists of a condensate of spin-singlets along the rungs of the ladder. We generalize this approach to larger angular-momentum coupled bases which incorporate---by their mere definition---a substantial fraction of the important short-range structure of these materials. In these bases the mean-field ground-state remains a condensate of spin singlet---but now with each involving a larger fraction of the spins in the ladder. As expected, the ``purity'' of the ground-state, as judged by the condensate fraction, increases with the size of the elementary block defining the basis. Moreover, the coupling to quasiparticle excitations becomes weaker as the size of the elementary block increases. Thus, the weak-coupling limit of the theory becomes an accurate representation of the underlying mean-field dynamics. We illustrate the method by computing static and dynamic properties of two-leg ladders in the various angular-momentum coupled bases.