Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry

Abstract

We numerically study quantum magnetism of ultra-cold alkali and alkaline-earth fermion systems with large hyperfine spin $F=3/2$, which are characterized by a generic $Sp(N)$ symmetry with N=4. The methods of exact diagonalization (ED) and density-matrix-renormalization-group are employed for the large size one-dimensional (1D) systems, and ED is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges $J_0$ and $J_2$ in the bond spin singlet and quintet channels, respectively. In 1D, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at $J_0/J_2>1$, and a gapless spin liquid state at $J_0/J_2\le 1$, respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In 2D, various spin correlation functions are calculated up to the size of $4\times 4$. The Neel-type spin correlation dominates at large values of $J_0/J_2$, while a $2\times 2$ plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competitions among the plaquette ordering, the dimer ordering, and the Neel ordering in the 2D system.

16 pages

References in corpus (24)

• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Fermi liquid instabilities in the spin channel
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Heavy electrons and the symplectic symmetry of spin
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• Resonating plaquette phases in large spin cold atom systems
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Symplectic N and time reversal in frustrated magnetism
• Exact spontaneous plaquette ground states for high-spin ladder models
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• Search for quantum dimer phases and transitions in a frustrated spin ladder
• Exotic many-body physics with large-spin Fermi gases
• Spectral convexity for attractive SU(2N) fermions
• Resonating singlet valence plaquettes
• Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Continuous quantum phase transition between two topologically distinct valence bond solid states associated with the same spin value
• Mott insulating phases and quantum phase transitions of interacting spin-3/2 fermionic cold atoms in optical lattices at half filling
• Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice
• Exact models for trimerization and tetramerization in spin chains
• Topological term in the non-linear $\sigma$ model of the SO(5) spin chains

Cited by in corpus (13)

• Spin-orbital quantum liquid on the honeycomb lattice
• Production of quantum degenerate strontium gases: Larger, better, faster, colder
• On topological phases of spin chains
• SO(5) symmetry in the quantum Hall effect in graphene
• Reservoir spectroscopy of 5s5p ${}^3$P${}_2$ - 5s$n$d ${}^3$D${}_{1,2,3}$ transitions in strontium
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• The Symmetry Principle in Condensed Matter Physics (I)
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice