Variational Monte-Carlo investigation of SU($N$) Heisenberg chains

TL;DR

This study uses variational Monte Carlo to analyze SU(N) Heisenberg chains, confirming theoretical predictions about ground state properties and uncovering critical states in marginal cases, relevant for cold atom experiments.

Contribution

It provides the first comprehensive numerical verification of bosonization predictions for SU(N) chains with N up to 10 and m up to N/2, including critical and gapped phases.

Findings

Gapped phases associated with dimerization or trimerization.

Critical ground states in marginal cases with conformal field theory exponents.

Verification of bosonization predictions for N ≤ 10 and m ≤ N/2.

Abstract

Motivated by recent experimental progress in the context of ultra-cold multi-color 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, Nuclear Physics B 265, 409 (1986); 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 $N \leq 10$ and $m \leq N/2$, 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.