Related papers: The 1-2 model
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the…
The vertex-cover problem is studied for random graphs $G_{N,cN}$ having $N$ vertices and $cN$ edges. Exact numerical results are obtained by a branch-and-bound algorithm. It is found that a transition in the coverability at a $c$-dependent…
Using the monomer--dimer representation of the lattice Schwinger model, with $N_f =1$ Wilson fermions in the strong--coupling regime ($\beta=0$), we evaluate its partition function, $Z$, exactly on finite lattices. By studying the zeroes of…
The model of lattice fermions in 2+1 dimensional space is formulated, the critical states of which are lying in the basis of such physical problems, as 3D Ising Model(3DIM) and the edge excitations in the Hall effect. The action for this…
We examine a periodic mixed spin chain with spin magnitudes 1/2 and 1 which are arrayed as 1/2-1/2-1-1. The three independent parameters are ratios of the four exchange couplings. We determine phase boundaries in the parameter space by…
A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
We employ a plaquette basis-generated by coupling the four spins in a $2\times2$ lattice to a well-defined total angular momentum-for the study of Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the Hamiltonian in…
A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first…
Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…
Ground-state and finite-temperature behaviour of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on decorated planar lattices consisting of inter-connected diamonds is investigated by means of the generalised decoration-iteration…
Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the O$(n)$ models on the simple-cubic lattice with $n=1$, 2, and 3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we find…
We explore the ground-state physics of two-dimensional spin-$1/2$ $U(1)$ quantum link models, one of the simplest non-trivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the…
We study the dimer model on the square grid, with quenched random edge weights. Randomness is chosen to have a layered structure, similar to that of the celebrated McCoy-Wu disordered Ising model. Disorder has a highly non-trivial effect…
The $2$-star model is the simplest exponential random graph model that displays complex behavior, such as degeneracy and phase transition. Despite its importance, this model has been solved only in the regime of dense connectivity. In this…
The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 $J_{1}$--$J_{2}$ Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the…