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

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.

22 pages, 7 figs, added references to arxiv version

References in corpus (33)

• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Experimental realization of a 2D fractional quantum spin liquid
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• On the stability of U(1) spin liquids in two dimensions
• Ultracold fermions and the SU(N) Hubbard model
• Observation of extended scattering continua characteristic of spin fractionalization in the 2D frustrated quantum magnet Cs2CuCl4 by neutron scattering
• Algebraic spin liquid as the mother of many competing orders
• Projected Wavefunctions and High Temperature Superconductivity
• Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• High Tc Superconductors -- A Variational Theory of the Superconducting State
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Theory of spin excitations in undoped and underdoped cuprates
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Permanent confinement in the compact QED3 with fermionic matter
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Gossamer Superconductivity near Antiferromagnetic Mott Insulator in Layered Organic Conductors
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• Quantum Phase Transition in the SU(4) Spin-Orbital Model on the Triangular Lattice
• Relativity Restored: Dirac Anisotropy in QED${}_3$
• Mott transition and dimerization in the one-dimensional SU$(n)$ Hubbard model
• Absence of U(1) spin liquids in two dimensions
• Spin liquid correlations in Nd-langasite anisotropic Kagomé antiferromagnet
• Neel order, quantum spin liquids and quantum criticality in two dimensions
• Gauge invariant response functions in Algebraic Fermi liquids
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
• Resonating valence bond wave function for the two dimensional fractional spin liquid
• The Supersymmetric Ward-Takahashi Identity in 1-Loop Lattice Perturbation Theory. I. General Procedure
• Flavor Degeneracy and Effects of Disorder in Ultracold Atom Systems

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