Exact ground-state correlation functions of the one-dimensional strongly correlated electron models with the resonating-valence-bond ground state

TL;DR

This paper provides exact analytical expressions for correlation functions in one-dimensional strongly correlated electron models with resonating-valence-bond ground states, revealing exponential decay and insulating behavior due to strong correlations.

Contribution

It introduces a transfer matrix method with small matrices to exactly evaluate correlation functions in these models, highlighting the correlation-induced gap and insulating ground state.

Findings

Correlation functions decay exponentially with distance.

The models exhibit a finite excitation gap.

Persistent currents are exactly zero.

Abstract

We investigate the one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding non-interacting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.