Related papers: Parent Hamiltonians of Jastrow Wavefunctions
Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the…
In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $V(x)=\alpha x^{-2}$. In such a way, we have described…
We introduce a family of Jastrow pair product states for quasi one-dimensional spin systems. Depending on a parameter they interpolate between the resonating valence bond ground state of the Haldane-Shastry model describing a spin liquid…
Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen--Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series…
Infinite quasiperiodic arrangements in space, such as quasicrystals, are typically described as projections of higher-dimensional periodic lattices onto the physical dimension. The concept of a reference higher-dimensional space, called a…
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the…
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of…
The investigation of many-body interactions holds significant importance in both quantum foundations and information. Hamiltonians coupling multiple particles at once, beyond others, can lead to a faster entanglement generation, multiqubit…
We discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of $n>2$ non-relativistic quantum particles in dimension three with contact (or zero-range or $\delta$) interactions. Such interactions are…
We use path-\-integral methods to derive the ground state wave functions of a number of two-\-dimensional fermion field theories and related systems in one-\-dimensional many body physics. We derive the exact wave function for the…
We review a recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions, that can be used to generate "dynamically" a large family of curved spaces. From an algebraic viewpoint,…
The exchange operator formalism previously introduced for the Calogero problem is extended to the three-body Calogero-Marchioro-Wolfes one. In the absence of oscillator potential, the Hamiltonian of the latter is interpreted as a free…
We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified…
The one-dimensional system of particles with a $1/x^2$ repulsive potential is known as the Calogero-Moser system. Its classical version can be generalised by substituting the coupling constants with additional degrees of freedom, which span…
The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x{\rightarrow}\bar{x}^{\bar{\alpha}}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This…
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…
We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for…
We describe the computational ingredients for an approach to treat interacting fermion systems in the presence of pairing fields, based on path-integrals in the space of Hartree-Fock-Bogoliubov (HFB) wave functions. The path-integrals can…
We demonstrate how a one parameter family of interacting non-commuting Hamiltonians, which are physically equivalent, can be constructed in non-commutative quantum mechanics. This construction is carried out exactly (to all orders in the…
We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such Hamiltonian converges…