Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice

Abstract

We study the magnetic phase diagram of spin-3/2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large on-site repulsion the system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We analyze the Sp(N) spin model with the help of the large-N field-theoretical approach and show that the effective theory corresponds to the Sp(N) extension of the CP^{N-1} model, with the Lorentz invariance generically broken. We obtain the renormalization flow of the model couplings and show that although the Sp(N) terms are seemingly irrelevant, their presence leads to a renormalization of the CP^{N-1} part of the action, driving a phase transition. We further consider the influence of the external magnetic field (the quadratic Zeeman effect), and present the qualitative analysis of the ground state phase diagram.

10 Revtex pages, 5 figures; (v2) corrected the last paragraph in Appendix B and some typos; (v3) added references, extended discussion of the phase diagram

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• "Deconfined" quantum critical points
• Collisional stability of a three-component degenerate Fermi gas
• Degenerate Fermi Gases of Ytterbium
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Exact spontaneous plaquette ground states for high-spin ladder models
• Ground States of the SU(N) Heisenberg Model
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Valence bond solid states with symplectic symmetry
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
• Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling
• Quantum Phase Transitions beyond the Landau's Paradigm in Sp(4) Spin System

Cited by in corpus (3)

• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• The Symplectic Fermi Liquid and its realization in cold atomic systems
• $SU(N)\to SU(2)$ symmetry breaking in quantum antiferromagnets