Exact results for resonating valence bonds states on 2D (narrow) systems

TL;DR

This paper develops an exact transfer matrix approach to compute spin-spin correlations in resonating valence bond states on narrow 2D lattices, enabling precise numerical analysis of these quantum states.

Contribution

It introduces a transfer matrix method for exact calculation of correlations in RVB states on narrow 2D systems, extending computational capabilities.

Findings

Exact numerical results for spin-spin correlations on ladders up to four units wide.

Formulation of the problem in terms of a transfer matrix for efficient computation.

Application to possibly diluted 2D square lattices.

Abstract

It is shown that the problem of calculating spin-spin correlation functions, in the dimers RVB states, on a possibly diluted 2D square lattice, can be formulated in terms of a transfer matrix. The transfer matrix is used for exact numerical calculations of spin-spin correlation functions on ladders up to four units wide.