Related papers: A Quantum Many-body Problem in Two Dimensions: Gro…
We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the…
We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered (CO) ground states as the strength of the longer range…
Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly…
We consider the inverse problem of determining the coupling coefficients in a two-state Schr\"odinger system. We prove a Lipschitz stability inequality for the zeroth and first order coupling terms by finitely many partial lateral…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal…
We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a…
The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly…
Ground-state energies are investigated in a many-quark model with pairing interactions, which has the su(4)-algebraic structure. Exact eigenstates in the boson realization method are constructed by imposing a color-singlet condition…
We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two…
Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…
We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering…
Knowledge of all correlation functions of a system is equivalent to solving the corresponding many-body problem. Already a finite set of correlation functions can be sufficient to describe a quantum many-body system if correlations…
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational…
It has been shown that effective lowering of dimension underlies ground-state space structure and properties of two-dimensional lattice systems with a long-range interparticle repulsion. On the basis of this fact a rigorous general…
Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques…
We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The…
We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock…