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

Pierre Nataf and Frédéric Mila
Phys. Rev. B 97, 134420 – Published 20 April 2018

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.

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  • Received 15 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.134420

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Pierre Nataf1,2 and Frédéric Mila1

  • 1Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
  • 2Univiversité Grenoble Alpes, CEA INAC-PHELIQS, F-38000, Grenoble, France

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Issue

Vol. 97, Iss. 13 — 1 April 2018

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