Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
arXiv:1709.10326 · doi:10.1016/j.aop.2017.11.007
Abstract
We completely solve the problem of classifying all one-dimensional quantum potentials with nearest- and next-to-nearest-neighbors interactions whose ground state is Jastrow-like, i.e., of Jastrow type but depending only on differences of consecutive particles. In particular, we show that these models must necessarily contain a three-body interaction term, as was the case with all previously known examples. We discuss several particular instances of the general solution, including a new hyperbolic potential and a model with elliptic interactions which reduces to the known rational and trigonometric ones in appropriate limits.
arXiv commentTypeset in LaTeX, 18 pages, 7 figures
References in corpus (31)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Fractional Quantum Hall States and Jack Polynomials
- The Calogero-Sutherland Model and Generalized Classical Polynomials
- Physics and Mathematics of Calogero particles
- Black Holes and Calogero Models
- Lattice Integrable Systems of Haldane-Shastry Type
- Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
- Spectrum of a spin chain with inverse square exchange
- Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model
- Short-range plasma model for intermediate spectral statistics
- Random matrix theory and symmetric spaces
- Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
- An exactly solvable many-body problem in one dimension
- Calogero-Sutherland model and bulk-boundary correlations in conformal field theory
- A class of N-body problems with nearest- and next-to-nearest neighbour interactions
- Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
- Orthogonal Polynomials of Types A and B and Related Calogero Models
- Quantum Quench of the trap frequency in the harmonic Calogero model
- Correspondence between conformal field theory and Calogero-Sutherland model
- Loop groups, anyons and the Calogero-Sutherland model
- Random Matrix Model and the Calogero-Sutherland Model: A Novel Current-Density Mapping
- Higher rank Killing tensors and Calogero model
- The Heun equation and the Calogero-Moser-Sutherland system IV: the Hermite-Krichever Ansatz
- Truncated Calogero-Sutherland models
- Solvable scalar and spin models with near-neighbors interactions
- Exchange operator formalism for N-body spin models with near-neighbors interactions
- Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
- The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles
- Exact solution of a many body problem with nearest and next-nearest neighbour interactions
- A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
- Truncated Calogero-Sutherland Models on a Circle