Integrable spin- particle systems with long-range interactions

Kazuhiro Hikami, P. P. Kulish, Miki Wadati

Kazuhiro Hikami, Miki Wadati

Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with $\mathrm{SU}(\ensuremath{\nu})$ spins, a hidden symmetry is the $\mathrm{SU}(\ensuremath{\nu})\ensuremath{\bigotimes}\mathrm{U}(1)\ensuremath{\simeq}\mathrm{U}(\ensuremath{\nu})$ current algebra. The system has a higher symmetry, the ${W}_{1+\ensuremath{\infty}}$ algebra. This $W$ algebra structure unifies the Calogero type ($\frac{1}{{x}^{2}}$ interactions) and the Sutherland type ($\frac{1}{{sin}^{2}x}$ interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

Yupeng Wang, P. Schlottmann

We present the exact solution of two Heisenberg-liquid models of particles with arbitrary spin S interacting via a hyperbolic long-range potential. In one model the spin-spin coupling has the simple antiferromagnetic Heisenberg exchange form, while for the other model the interaction is of the ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz equations of these models have a similar structure to that of the Babujian-Takhatajan spin chain. We also conjecture the integrability of a third spin-lattice model with long-range interaction.

Filippo Caleca, Fabio Mezzacapo, Tommaso Roscilde

Quantum thermalization of closed systems -- i.e. the relaxation of local properties to their thermodynamic value along the Hamiltonian evolution -- is generically expected in non-integrable systems at finite energy density. In this work we show that quantum spin systems with at least one spin component coupled through long-range ferromagnetic interactions, and a second spin component coupled to a field, cannot in general thermalize to a paramagnetic state whenever they have a finite, negative energy per spin. The long-range interactions we consider decay as a power law of the distance, $\sim r^{-α}$ with $α< d$, where $d$ is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.

Manas Kulkarni, Fabio Franchini, Alexander G. Abanov

Kazuhiro Hikami, P. P. Kulish, Miki Wadati

Presented is a general method to construct quantum spin Hamiltonians with long-range pairwise interactions. The Hamiltonian is given explicitly in terms of the R -matrices on an inhomogeneous lattice. Applications to spin-1/2 chains, higher spin chains and Z n models are shown.