SU(N) quantum spin models: A variational wavefunction study

TL;DR

This paper employs Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlations of SU(N) quantum spin models in 1D and 2D, revealing various ordered and disordered phases and matching exact and large-N results.

Contribution

It introduces a variational wavefunction approach to study SU(N) spin models, providing detailed phase diagrams and correlation functions that align with known results and extend understanding of complex quantum phases.

Findings

In 1D, the variational phase diagram matches exact results.

In 2D, the ground state exhibits Neel order for N=2,4 and spin Peierls order for N>4.

The pi-flux state shows strong dimer correlations consistent with large-N calculations.

Abstract

The study of SU(N) quantum spin models is relevant to a variety of physical systems including ultracold atoms in optical lattices, and also leads to insights into novel quantum phases and phase transitions of SU(2) spin models. We use Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlation functions of SU(N) spin models in the self-conjugate representation, with Heisenberg bilinear and biquadratic interactions. In 1D, the variational phase diagram of the SU(4) spin chain is constructed by examining instabilities of the Gutzwiller projected free fermion ground state to various broken symmetries, and it agrees well with exact results.The spin and dimer correlations of the Gutzwiller projected free fermion state with N flavors of fermions are also in good agreement with exact and 1/N calculations for the critical points of SU(N) spin chains. In 2D, the variational phase diagram on the square lattice is obtained by studying instabilities of the Gutzwiller projected pi-flux state. The variational ground state of the pure Heisenberg model is found to exhibit long range Neel order for N=2,4 and spin Peierls order for N > 4. For N=4 and 6, biquadratic interactions lead to a complex phase diagram which includes an extended valence bond crystal in both cases, as well as a stable pi-flux phase for N=6. The spin correlations of the projected pi-flux state at N=4 are in good agreement with 1/N calculations. We find that this state also shows strongly enhanced dimer correlations, in qualitative accord with the large-N results. We compare our results with a recent QMC study of the SU(4) Heisenberg model.