Functionally independent conservations laws in a quantum integrable model
arXiv:1303.3526 · doi:10.1088/1751-8113/46/37/375003
Abstract
We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability.
5 pages
References in corpus (9)
- Nonequilibrium dynamics of closed interacting quantum systems
- Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
- Remarks on the notion of quantum integrability
- Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
- Measuring entanglement using quantum quenches
- Quantum integrability in systems with finite number of levels
- The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
- Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties
- Parameter Dependent Commuting Matrices, Plücker relations and Related Quantum Glass Models