Nonlinear dynamics of spin and charge in spin-Calogero model
arXiv:0904.3762 · doi:10.1103/PhysRevB.80.165105
Abstract
The fully nonlinear dynamics of spin and charge in spin-Calogero model is studied. The latter is an integrable one-dimensional model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. Classical hydrodynamic equations of motion are written for this model in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation variables separate in terms of dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi momenta. We study the dynamics of some non-equilibrium spin-charge configurations for times smaller than the time-scale of the gradient catastrophe. We find an interesting interplay between spin and charge degrees of freedom. In the limit of large coupling constant the hydrodynamics reduces to the spin hydrodynamics of the Haldane-Shastry model.
26 pages, 14 figures, 2 tables
References in corpus (4)
- Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
- Notes on Collective Field Theory of Matrix and Spin Calogero Models
- Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
- Emptiness and Depletion Formation Probability in spin models with inverse square interaction
Cited by in corpus (9)
- One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
- Quantum Generalized Hydrodynamics
- Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics
- Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics
- Spin generalizations of the Benjamin-Ono equation
- Cold Fermi-gas with long range interaction in a harmonic trap
- The non-chiral intermediate Heisenberg ferromagnet equation
- Emptiness and Depletion Formation Probability in spin models with inverse square interaction
- Emptiness Formation in Polytropic Quantum Liquids