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

TL;DR

This paper investigates quantum magnetism in ultra-cold fermion systems with symplectic symmetry, revealing diverse magnetic phases and correlations in 1D and 2D models through numerical methods.

Contribution

It provides the first detailed numerical analysis of $Sp(N)$ symmetric fermion systems, uncovering their rich phase diagrams and magnetic ordering behaviors.

Findings

1D systems show long-range dimerization and gapless spin liquid states.

2D systems exhibit Neel, plaquette, and dimer correlations depending on exchange ratios.

Multiple competing magnetic orders are identified in 2D lattice models.

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.