Related papers: Exact solution of a cluster model with next-neares…
The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the…
We introduce a class of spin models with long-range interactions---in the sense that they extend significantly beyond nearest neighbors---whose ground states can be constructed analytically and have a simple matrix product state…
We investigate the $J_1$-$J_2$ spin chain consisting of spins with magnitude $\frac12$. The nearest-neighbor and the next-nearest-neighbor exchange interactions are ferromagnetic and antiferromagnetic, respectively, and induce strong…
An exactly solvable model of a quantum spin interacting with a spin environment is considered. The interaction is chosen to be such that the state of the environment is conserved. The reduced density matrix of the spin is calculated for…
In the paper the thermodynamics of a cubic cluster with 8 sites at quarter filling is characterized by means of exact diagonalization technique. Particular emphasis is put on the behaviour of such response functions as specific heat and…
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated…
Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
We present a class of exactly solvable quantum spin models which consist of two Heisenberg-subsystems coupled via a long-range Lieb-Mattis interaction. The total system is exactly solvable whenever the individual subsystems are solvable and…
A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an…
The model considered is a d=2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are…
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…
We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It…
We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ…
We present a new class of exact self-similar solutions possessing cylindrical or spherical symmetry in Born-Infeld theory. A cylindrically symmetric solution describes the propagation of a cylindrical electromagnetic disturbance in a…
We introduce a family of spin-1/2 quantum chains, and show that their exact ground states break the rotational and translational symmetries of the original Hamiltonian. We also show how one can use projection to construct a spin-3/2 quantum…
We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We…
We consider trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. The exact ground state energy and wave function are identified in closed form together with a rich phase…
We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-length vectorial spins, with random pair-interactions which are of the orthogonal matrix type. Since the spins are continuous and the…
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors.…