DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz

TL;DR

This paper introduces an efficient SU(N) symmetric DMRG method for Heisenberg chains, benchmarks it against Bethe ansatz results up to N=8, and confirms theoretical predictions for entanglement properties.

Contribution

It extends DMRG techniques using Young tableaux for SU(N) chains and provides high-precision benchmarks against Bethe ansatz solutions.

Findings

Ground state energy matches Bethe ansatz with high accuracy for N=3 to 8.

Entanglement entropy results agree with SU(N)1 Wess-Zumino-Witten CFT predictions.

Method efficiently handles large systems up to 420 sites with full SU(N) symmetry.

Abstract

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N) Heisenberg chain with open boundary conditions taking full advantage of the SU(N) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e. one particle per site in the fermionic formulation), we have benchmarked our results for the ground state energy up to N = 8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N = 8 (6 digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula, and agree with the theoretical values expected from the SU(N)1 Wess-Zumino-Witten CFTs.