Density matrix renormalization group simulations of SU( N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

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 (six 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 conformal field theories.
Type de document :
Article dans une revue
Phys.Rev.B, 2018, 97 (13), pp.134420. 〈10.1103/PhysRevB.97.134420〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01730040
Contributeur : Inspire Hep <>
Soumis le : lundi 12 mars 2018 - 20:41:48
Dernière modification le : lundi 18 juin 2018 - 18:24:21

Lien texte intégral

Identifiants

Collections

Citation

Pierre Nataf, Frédéric Mila. Density matrix renormalization group simulations of SU( N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz. Phys.Rev.B, 2018, 97 (13), pp.134420. 〈10.1103/PhysRevB.97.134420〉. 〈hal-01730040〉

Partager

Métriques

Consultations de la notice

40