# Integrable systems for particles with internal degrees of freedom

@article{Minahan1993IntegrableSF, title={Integrable systems for particles with internal degrees of freedom}, author={Joseph A. Minahan and Alexios P. Polychronakos}, journal={Physics Letters B}, year={1993}, volume={302}, pages={265-270} }

Abstract We show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently developed exchange operator formalism. This allows us to construct the invariants of the motion for these systems. We also calculate the wave-functions for the Calogero-like models in the ferromagnetic and antiferromagnetic regimes.

## 123 Citations

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We present a detailed analysis of the spin models with near-neighbours interactions constructed in our previous paper (Enciso et al 2005 Phys. Lett. B 605 214) by a suitable generalization of the…

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## References

SHOWING 1-10 OF 23 REFERENCES

Exchange operator formalism for integrable systems of particles.

- Physics, MedicinePhysical review letters
- 1992

One-dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators assuming a decoupled form greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.

A new integrable system with a quartic potential

- Physics
- 1992

Abstract We show that a system of particles on the line in an arbitrary quartic external potential and interacting through two-body inverse square potentials is integrable. This result generalizes…

Integrable systems from gauged matrix models

- Physics
- 1991

Abstract We show that integrable systems of the Calogero type and its generalizations can be obtained from gauged one-dimensional matrix models including a fermionic part and a Chern-Simons term. The…

New integrable systems from unitary matrix models

- Physics
- 1991

Abstract We show that the one-dimensional unitary matrix model with potential of the form aU + bU 2 +h.c. is integrable. By reduction to the dynamics of the eigenvalues, we establish the…

Three integrable Hamiltonian systems connected with isospectral deformations

- Mathematics
- 1975

Publisher Summary This chapter discusses three integrable hamiltonian systems connected with isospectral deformations. In recent years, various phenomena have been discovered that are clearly…

Exact results for a quantum many body problem in one-dimension

- Physics
- 1971

We continue our previous investigation of the properties of a system of either fermions or bosons interacting in one dimension by a two-body potential $V(\mathcal{r})=\frac{g}{{\mathcal{r}}^{2}}$…

Asymptotic Bethe-ansatz solution of multicomponent quantum systems with 1/r2 long-range interaction.

- Physics, MedicinePhysical review. B, Condensed matter
- 1992

Asymptotic Bethe-ansatz solutions are obtained for one-dimensional quantum systems with a 1/r 2 long-range interaction by generalizing Sutherland's method to multicomponent quantum systems. We obtain…

Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions.

- Physics, MedicinePhysical review letters
- 1988

The S=½ Heisenberg Hamiltonian H = ½ N - 1Σn = 1NΣm = 1 Jn σM · σm+n with Jn=J0/sin2 (nπ/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and…

SU(N) generalization of the Gutzwiller-Jastrow wave function and its critical properties in one dimension.

- Physics, MedicinePhysical review. B, Condensed matter
- 1992

The SU(N)-generalized Gutzwiller-Jastrow wave function, which includes the effects of smooth-correlation holes, is discussed in one dimension and the universal scaling relations for SU (N) Luttinger liquids are derived.

Ground State of a One‐Dimensional N‐Body System

- Physics
- 1969

The problem of N quantum‐mechanical equal particles interacting pairwise by inverse‐cube forces (``centrifugal potential'') in addition to linear forces (``harmonical potential'') is considered in a…