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

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 $N\le 10$ and $m\le N/2$, 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.

arXiv comment9 pages, 10 figures, 3 tables

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• Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Massless renormalization group flow in SU(N)${}_k$ perturbed conformal field theory
• Linear Flavor-Wave Theory for Fully Antisymmetric $\mathrm{SU}(N)$ Irreducible Representations
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Impenetrable SU(N) fermions in one-dimensional lattices
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Stabilization of the chiral phase of the SU($6m$) Heisenberg model on the honeycomb lattice with $m$ particles per site for $m$ larger than 1
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Ground state separability and criticality in interacting many-particle systems
• Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach