Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice

TL;DR

This study maps the ground-state phases of the SU(4) Heisenberg model on a plaquette lattice, revealing a transition from a singlet state to coexisting magnetic orders as anisotropy varies, with implications for ultracold atom experiments.

Contribution

It provides the first detailed phase diagram of the SU(4) Heisenberg model on a plaquette lattice using tensor-network methods, identifying the nature and location of phase transitions.

Findings

SU(4) singlet ground state in the strongly anisotropic limit

Coexistence of Néel and valence-bond crystal orders near isotropy

First-order phase transition around J'/J ≈ 0.85(5)

Abstract

We investigate the ground state of the SU($4$) Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the SU($4$) singlet ground state appears in the strongly anisotropic limit, whereas N\'eel and valence-bond crystal orders coexist in the nearly isotropic limit. By examining the intermediate parameter region, we identify a phase transition between these phases. The nature of the phase transition is likely to be of first order, and the transition point is estimated to be around $J'/J\approx 0.85(5)$, where $J$ and $J'$ are the interaction strengths of intra- and interplaquette bonds, respectively. We also calculate the anisotropy dependence of singlet correlations on a plaquette bond, which will be useful for future experiments of ultracold atoms in optical lattices.