A systematic and unifying method is developed and demonstrated for obtaining exact solutions of n-site (n even integer) Ising correlations on various planar lattices. The scheme, which is exceedingly more simple than using solely traditional Pfaffian techniques, embodies five mapping theorems in alliance with algebraic correlation identities. In the theoretical framework, the triangular Ising model plays an overarching role. In particular, considering a select 7-site cluster of the triangular Ising model, the knowledge of all its 11 even-number correlations defined upon this cluster (where only four of the correlations need to be actually calculated by Pfaffian procedures) is shown to be sufficient for determining exactly all honeycomb, decorated-honeycomb, and kagom\'e Ising model even-number correlations upon their correspondingly select 10-site, 19-site, and 9-site clusters, respectively. The relative ease and direct applicability of the present approach are highlighted not only by the resulting large numbers of n-site (n even-integer) correlation solutions (e.g., approximately 85 and 50 for the honeycomb and kagom\'e Ising models, respectively) and their large ${n}_{\mathrm{max}}$ values ( ${n}_{\mathrm{max}=8}$ ,10,18 for the kagom\'e, honeycomb, and decorated-honeycomb Ising models, respectively) but also by the realization that the exact solutions for Ising multisite correlations upon the kagom\'e lattice (one of the four regular lattices in two dimensions) are apparently the first to explicitly appear in the literature beyond its nearest-neighbor pair correlation (energy).A systematic and unifying method is developed and demonstrated for obtaining exact solutions of n-site (n even integer) Ising correlations on various planar lattices. The scheme, which is exceedingly more simple than using solely traditional Pfaffian techniques, embodies five mapping theorems in alliance with algebraic correlation identities. In the theoretical framework, the triangular Ising model plays an overarching role. In particular, considering a select 7-site cluster of the triangular Ising model, the knowledge of all its 11 even-number correlations defined upon this cluster (where only four of the correlations need to be actually calculated by Pfaffian procedures) is shown to be sufficient for determining exactly all honeycomb, decorated-honeycomb, and kagom\'e Ising model even-number correlations upon their correspondingly select 10-site, 19-site, and 9-site clusters, respectively. The relative ease and direct applicability of the present approach are highlighted not only by the resulting large numbers of n-site (n even-integer) correlation solutions (e.g., approximately 85 and 50 for the honeycomb and kagom\'e Ising models, respectively) and their large ${n}_{\mathrm{max}}$ values (${n}_{\mathrm{max}=8}$,10,18 for the kagom\'e, honeycomb, and decorated-honeycomb Ising models, respectively) but also by the realization that the exact solutions for Ising multisite correlations upon the kagom\'e lattice (one of the four regular lattices in two dimensions) are apparently the first to explicitly appear in the literature beyond its nearest-neighbor pair correlation (energy).

Physical review. B, Condensed matterApr 1, 198856 citations

Optically induced reconfigurable Kagome photonic lattice assisted by a liquid crystal spatial light modulator

Shun Ke Liang, Zhenzhi Liu, Jiawei Yu +4 more

A 2D Kagome photonic lattice possesses special band structures involving a flat band that allows the localization state and Dirac cones that show linear dispersion. Here, we report the construction of an instantaneously reconfigurable electromagnetically induced Kagome lattice in a Λ-type 85 Rb atomic configuration theoretically and experimentally under the condition of electromagnetically induced transparency, which is excited by a weak Gaussian probe field and a strong coupling field with a Kagome intensity profile. The incident Gaussian probe field is discretely diffracted into a Kagome profile inside the atomic vapor cell with a spatially modulated susceptibility, which is induced by the structured coupling field generated by a liquid crystal spatial light modulator. We also explored the dynamical evolution of the probe field inside the Kagome photonic lattice by manipulating systematic parameters. This current work provides an alternative way to design instantaneously reconfigurable Kagome photonic lattices with a simplified experimental configuration. The instantaneous tunability may help to promote the discovery of underlying beam dynamics and the design of tunable devices relying on the properties of Kagome photonic structures.A 2D Kagome photonic lattice possesses special band structures involving a flat band that allows the localization state and Dirac cones that show linear dispersion. Here, we report the construction of an instantaneously reconfigurable electromagnetically induced Kagome lattice in a Λ-type 85 Rb atomic configuration theoretically and experimentally under the condition of electromagnetically induced transparency, which is excited by a weak Gaussian probe field and a strong coupling field with a Kagome intensity profile. The incident Gaussian probe field is discretely diffracted into a Kagome profile inside the atomic vapor cell with a spatially modulated susceptibility, which is induced by the structured coupling field generated by a liquid crystal spatial light modulator. We also explored the dynamical evolution of the probe field inside the Kagome photonic lattice by manipulating systematic parameters. This current work provides an alternative way to design instantaneously reconfigurable Kagome photonic lattices with a simplified experimental configuration. The instantaneous tunability may help to promote the discovery of underlying beam dynamics and the design of tunable devices relying on the properties of Kagome photonic structures.

Journal of the Optical Society of America BMay 9, 20233 citations

Models for Strongly Correlated Lattice Physics

Michael L. Wall

Springer thesesJan 1, 20150 citations

Quantum Correlations of Toda Lattice

Alessandro Cuccoli, M. Spicci, V. Tognetti +1 more

NATO ASI series. Series B : PhysicsJan 1, 19940 citations

Tripartite entangled plaquette state in a cluster magnet

Juan Carrasquilla, Gang Chen, Roger G. Melko

Using large-scale quantum Monte Carlo simulations we show that a spin- $\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ$ model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break $U(1)$ and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ , as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.Using large-scale quantum Monte Carlo simulations we show that a spin-$\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ$ model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break $U(1)$ and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.

arXiv:1704.03478Physical review. B./Physical review. BAug 4, 201717 citations

{n}_{\mathrm{max}}

values (

{n}_{\mathrm{max}=8}

,10,18 for the kagom\'e, honeycomb, and decorated-honeycomb Ising models, respectively) but also by the realization that the exact solutions for Ising multisite correlations upon the kagom\'e lattice (one of the four regular lattices in two dimensions) are apparently the first to explicitly appear in the literature beyond its nearest-neighbor pair correlation (energy).

Using large-scale quantum Monte Carlo simulations we show that a spin-

\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ

model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break

U(1)

and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate

{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}

, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.