Exact wave functions and entropies of the one dimensional Regularized Calogero model
arXiv:1709.06374 · doi:10.1088/1751-8121/aab85e
Abstract
The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's polynomials. It is shown both, analytical and numerically. that the reduced density matrix obtained tracing out one particle from the two-particle density operator can be obtained exactly as well as its entanglement spectrum. The number of non-zero eigenvalues in these cases is finite. Besides, it is shown that taking the limit in which the cutoff distance goes to zero, the reduced density matrix and finite entanglement spectrum of the Calogero model is retrieved. The entanglement Rényi entropy is also studied to characterize the physical traits of the model. It is found that the quasi-exactly solvable character of the model is put into evidence by the entanglement entropies when they are calculated numerically over the parameter space of the model.
References in corpus (20)
- Lattice Integrable Systems of Haldane-Shastry Type
- Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
- Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
- On a solution of the Schrodinger equation with a hyperbolic double-well potential
- Pinning of Fermionic Occupation Numbers
- Two electrons on a hypersphere: a quasi-exactly solvable model
- Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model
- Complex Calogero model with real energies
- Application of the confluent Heun functions for finding the quasinormal modes of nonrotating black holes
- Quasi-pinning and entanglement in the lithium isoelectronic series
- Magnetic quantum dots and rings in two dimensions
- Natural occupation numbers: When do they vanish?
- Generalized Calogero models through reductions by discrete symmetries
- Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
- Entanglement Entropy in the Calogero-Sutherland Model
- Generalized local-density approximation and one-dimensional finite uniform electron gases
- Assessment of density functional approximations: long-range correlations and self-interaction effects
- Two-electron atom with a screened interaction
- Deformed Calogero-Sutherland model and fractional Quantum Hall effect
- Detecting dimensional crossover and finite Hilbert space through entanglement entropies