Integrability and explicit solutions to nonuniform quantum spin lattices

Zhihuan Luo, Casey Berger, Joaquín E. Drut

We study harmonically trapped, unpolarized fermion systems with attractive interactions in two spatial dimensions with spin degeneracies ${N}_{f}^{}=2$ and 4 and $N/{N}_{f}^{}=1,\phantom{\rule{0.28em}{0ex}}3,\phantom{\rule{0.28em}{0ex}}5$, and 7 particles per flavor. We carry out our calculations using our recently proposed quantum Monte Carlo method on a nonuniform lattice. We report on the ground-state energy and contact for a range of couplings, as determined by the binding energy of the two-body system, and show explicitly how the physics of the ${N}_{f}$-body sector dominates as the coupling is increased.

Harald Grosse, Karl-Georg Schlesinger

V. I. Inozemtsev

Amir Aghamohammadi, Cina Aghamohammadi, Mohammad Khorrami

A one dimensional kinetic Ising model at a finite temperature on a semi-infinite lattice with time varying boundary spins is considered. Exact expressions for the expectation values of the spin at each site are obtained, in terms of the time dependent boundary condition and the initial conditions. The solution consists of a transient part which is due to the initial condition, and a part driven by the boundary. The latter is an evanescent wave when the boundary spin is oscillating harmonically. Low- and high-frequency limits are investigated with greater detail. The total magnetization of the lattice is also obtained. It is seen that for any arbitrary rapidly varying boundary conditions, this total magnetization is equal to the the boundary spin itself, plus essentially the time integral of the boundary spin. A nonuniform model is also investigated.

Anjan Kundu

A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through twisting transformation. The models belong to quantum integrable systems allowing explicit R-matrix solution. The eigenvalue problem can be solved exactly using some symmetry of the models.

Stefan Weigert, Gerhard H. Muller