A spin-1 atomic gas in an optical lattice, in the unit-filling Mott insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a nonvanishing value of the spin glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. We also study the distribution of the block entanglement entropy in the different regions.A spin-1 atomic gas in an optical lattice, in the unit-filling Mott insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a nonvanishing value of the spin glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. We also study the distribution of the block entanglement entropy in the different regions.

arXiv:1702.01765Physical review. B./Physical review. BJun 15, 20178 citations

Spin-glass properties of ± J random-bond model

Hiroshi Betsuyaku

Journal of Magnetism and Magnetic MaterialsFeb 1, 19832 citations

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

Anirudha Menon, Tom Pardini, Rajiv R. P. Singh

We study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to $N=64$ site systems. We calculate spin-glass correlation functions and local entanglement entropy ${S}_{T}$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where ${S}_{T}=ln6$ . Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and ${S}_{T}=ln2$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.We study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to $N=64$ site systems. We calculate spin-glass correlation functions and local entanglement entropy ${S}_{T}$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where ${S}_{T}=ln6$. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and ${S}_{T}=ln2$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

arXiv:1911.10243Physical review. B./Physical review. BMay 21, 20202 citations

On biquadratic exchange interactions in spin-1 systems

H. H. Chen

Physics Letters ADec 1, 19741 citation

Critical Properties of a Simple Spin Glass Model

Amnon Aharony A, Y. Imry

Springer eBooksJan 1, 19770 citations

N=64

site systems. We calculate spin-glass correlation functions and local entanglement entropy

{S}_{T}

between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where

{S}_{T}=ln6

. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and

{S}_{T}=ln2

corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.