# One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable.

@article{Yang2022OneDimensionalQS, title={One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable.}, author={Jing Yang and Adolfo del Campo}, journal={Physical review letters}, year={2022}, volume={129 15}, pages={ 150601 } }

Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by exchange operator formalism and the complete infinite family of parent Hamiltonians describing quantum many-body models with ground states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the family and establish its integrability, even…

## References

SHOWING 1-10 OF 24 REFERENCES

### Exact results in quantum many‐body systems of interacting particles in many dimensions with SU(1,2)¯ (1̄,1̄) as the dynamical group

- Physics, Mathematics
- 1975

We consider a class of system of N interacting particles in any dimension—the potential includes a quadratic pair potential and an arbitrary translation‐invariant position‐dependent potential that is…

### Quantum Many‐Body Problem in One Dimension: Thermodynamics

- Physics, Mathematics
- 1971

We continue our investigation of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. We first present an approximation for the eigenstates of a…

### Three integrable Hamiltonian systems connected with isospectral deformations

- Mathematics, Physics
- 1975

### Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension

- Physics
- 1960

A rigorous one‐one correspondence is established between one‐dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle…

### Quantum many body problem in one-dimension: Ground state

- Physics
- 1971

We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state…

### Exchange interactions, Yang-Baxter relations and transparent particles

- MathematicsNuclear Physics B
- 2020

### The Bethe Wavefunction

- Physics
- 2014

Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first…

### Tonks–Girardeau gas of ultracold atoms in an optical lattice

- PhysicsNature
- 2004

A theoretical prediction of the momentum distribution is made based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.