Contractor renormalization group theory of the SU($N$) chains and ladders

TL;DR

This paper applies the contractor renormalization group (CORE) method to SU(N) chains and ladders, demonstrating how these systems can be analyzed through iterative transformations to determine ground state energies and energy gaps.

Contribution

The paper introduces a CORE scheme that preserves the Hamiltonian form for SU(N) chains and ladders, enabling analysis of their ground states and energy gaps.

Findings

SU(N) chains' ground state energy matches Bethe ansatz results

Spin-1/2 ladders exhibit a finite energy gap

Application to SU(3) ladders discussed

Abstract

Contractor renormalization group (CORE) method is applied to the SU($N$) chain and ladders in this paper. In our designed schemes, we show that these two classes of systems can return to their original form of Hamiltonian after CORE transformation. Successive iteration of the transformation leads to a fixed point so that the ground state energy and the energy gap to the ground state can be deduced. The result of SU($N$) chain is compared with the one by Bethe ansatz method. The transformation on spin-1/2 ladders gives a finite gap in the excited energy spectra to the ground state in an intuitive way. The application to SU(3) ladders is also discussed.