Renormalization group method for weakly coupled quantum chains: comparison with exact diagonalization

TL;DR

This paper demonstrates that a numerical renormalization group approach effectively studies weakly coupled quantum chains, showing high accuracy especially in frustrated systems, with results comparable to exact diagonalization.

Contribution

It introduces a quasi-one-dimensional renormalization group method for weakly coupled chains and systematically compares its accuracy with exact diagonalization results.

Findings

High accuracy in weakly coupled chains

Method performs well with frustrated systems

Accuracy improves with larger eigenstate basis

Abstract

We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates of the density matrix defined in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We also show that the method performs especially well in frustrated systems.