Phase diagram of the spin-orbital model on the square lattice

Abstract

We study the phase diagram of the spin-orbital model in both the weak and strong limits of the quartic spin-orbital exchange interaction. This allows us to study quantum phase transitions in the model and to approach from both sides the most interesting intermediate-coupling regime and in particular the SU (4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al [Phys. Rev. Lett. 81, 3527 (1999)] that at this point the ground state of the system is a plaquette spin-orbital liquid. We argue that the state is more complex. There is plaquette order, but it is anisotropic: bonds in one direction are stronger than those in the perpendicular direction. This order is somewhat similar to that found recently in the frustrated J1 − J2 Heisenberg spin model. 75.10.Jm, 75.40.Gb

Two-orbital S U(N) magnetism with ultracold alkaline-earth atoms

“…We first describe how to prepare an array of independent double wells in the state |e, ↑ L |g, ↓ R , which we use for the proof-of-principle experiment to probe the spin-orbital interactions in the Kugel-Khomskii model [95,96,97,98,99,100,101]. After loading a band insulator of |g, ↓ atoms in a deep optical lattice, an additional lattice for both g (green) and e (yellow) atoms with twice the spacing of the first lattice is turned on in one direction to create an array of independent double wells [62].…”

Long-range order in the ground state of spin systems with orbital degeneracy

“…26 -28 The recent results of approximation methods also suggested that the ground state around the SU͑4͒ symmetric point with K ϭϪ4 is disordered. 29,30 In particular, a Schwinger-boson mean-field theory predicted that disordered ground states are still stable in three dimensions for some interval in the region KϽ0, IϭJϭ1, ⌬ϭ1. 30 The two-dimensional system at SU͑4͒ symmetric point with Kϭ4 is shown to be a disordered ground state with a gapful energy excitation by the Monte Carlo method; 28 thus the ground state in the vicinity of this SU͑4͒ symmetric point is thought to be disordered.…”

“…These behaviors are in contrast to the SU͑2͒ antiferromagnetic Heisenberg model having a Néel-ordered ground state in two or more dimensions. However, as was pointed out by some authors, the mean-field-type approximation methods contain an uncontrolled accuracy, 29 and for the numerical studies of two-and three-dimensional systems, those system sizes are not enough compared with those of onedimensional systems due to the large degrees of freedom of this system 25 and a minus sign problem. 31 Although the above studies have these difficulties, for the two-dimensional systems at both SU͑4͒ symmetric points and around it, almost all the results support the disordered ground state.…”

Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

“…One has to keep in mind that our construction of smooth fields becomes increasingly inadequate as J → 0; however, one can argue that the theory still remains valid at the energy scales of less than order J. Several numerical results using exact diagonalization on small 2d clusters, 42 series expansions, 43 and density matrix renormalization group (DMRG) on a ladder 44 suggest that the uniform SU (4) antiferromagnet (J = 0, λ = 1) is in a VBS phase with the plaquette-type dimerization order. At the same time, theoretical studies advocate different scenarios for the uniform SU (N ) antiferromagnetic point: in a recent work based on the Majorana fermion representation of spin-orbital operators, 45 the existence of a Z 2 spin-orbital liquid state with emergent nodal fermions has been proposed for N = 4; other studies based on Schwinger-boson representations 46,47 and exact diagonalization for the SU (3) case 47 suggest that at this point the ground state has the Néel-type Nsublattice order, which may be viewed as order at the wavevector (2π/N, 2π/N ).…”