Related papers: Exactly solvable random matrix models with additio…
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…
Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that $N$-body systems with two-body zero-range interactions can be treated reliably and efficiently by the…
We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one…
We propose a new quantum simulation method for simulating N-body interactions, which are tensor products of N Pauli operators, in an analytically exact manner. This method iteratively attaches many two-body interactions on one two-body…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyze in detail the…
We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $\gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert…
This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
The Hamiltonian H of one-body Maryland model is defined as the sum of a linear unperturbed Hamiltonian H_0 and the interaction V, which is a Toeplitz matrix. Maryland model with a doubly infinite Hilbert space are exactly solved. Special…
We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of…
There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this…
We present a relativistic treatment of the problem of soft electromagnetic structure by the modified instant form of relativistic Hamiltonian dynamics. Our approach uses relativistic parametrization and so picks out the relativistic…
We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
We study a two-dimensional model of topological superconductor with equal spin pairing and repulsive Hubbard interaction. When the pairing gap equals to the hopping constant, half of the spectrum of this model are flat bands, which makes…
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are…
Exact quantum integrability is established for a class of multi-chain electron models with correlated hopping and spin models with interchain interactions, by constructing the related Lax operators and R-matrices through twisting and gauge…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…