Variational Monte Carlo investigation of SU(N) Heisenberg chains

Jérôme Dufour, Pierre Nataf, and Frédéric Mila
Phys. Rev. B 91, 174427 – Published 26 May 2015

Abstract

Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU(N) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with m<N particles per site. These models have been studied for arbitrary N and m with non-Abelian bosonization [I. Affleck, Nucl. Phys. B 265, 409 (1986); I. Affleck, Nucl. Phys. B 305, 582 (1988)], leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. Using exact diagonalization and variational Monte Carlo based on Gutzwiller projected fermionic wave functions, we have been able to verify these predictions for a representative number of cases with N10 and mN/2, and we have shown that the opening of a gap is associated to a spontaneous dimerization or trimerization depending on the value of m and N. We have also investigated the marginal cases where Abelian bosonization did not lead to any prediction. In these cases, variational Monte Carlo predicts that the ground state is critical with exponents consistent with conformal field theory.

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  • Received 6 February 2015
  • Revised 4 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.174427

©2015 American Physical Society

Authors & Affiliations

Jérôme Dufour, Pierre Nataf, and Frédéric Mila

  • Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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Issue

Vol. 91, Iss. 17 — 1 May 2015

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