相关论文: Spin models of Calogero-Sutherland type and associ…
We compute the symplectic structure of the spin Calogero model in terms of algebro-geometric data on the associated spectral curve.
We present a construction of an integrable model as a projective type limit of Calogero-Sutherland models of $N$ fermionic particles, when $N$ tends to infinity. Explicit formulas for limits of Dunkl operators and of commuting Hamiltonians…
We discuss the behavior of the Calogero model and the related model of deformed oscillators with the S_N extended Heisenberg algebra for a special value of the constant of interaction/statistical parameter nu. The problem with finite number…
The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the…
We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another…
Exact coherent states in the Calogero-Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a…
We study an exactly solvable spin-orbital model that can be regarded as a classical analogue of the celebrated Kitaev honeycomb model and describes interactions between Rydberg atoms on the ruby lattice. We leverage its local and nonlocal…
As is well known, multivariate Rogers-Szeg\"o polynomials are closely connected with the partition functions of the $A_{N-1}$ type of Polychronakos spin chains having long-range interactions. Applying the `freezing trick', here we derive…
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the…
We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion,…
We briefly review models of relativistic particles with spin. Departing from the oldest attempts to describe the spin within the lagrangian framework we pass through various non supersymmetric models. Then the component and superfield…
I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of…
The frustrated spin-one-half Heisenberg model on triangualr and Kagome Lattices is mapped onto a single specis of fermion carrying statistical flux. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to…
The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a…
We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable…
We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to the branched polymers. We also show that by suitably modifying this model one can also obtain…
We diagonalize the XX model with a finite number of spins and periodic boundary conditions. We solve for the ground state, focus on the rapidity of the convergence to the thermodynamic limit and study the features of multipartite…
The ultraviolet structure of the Calogero-Sutherland models is examined, and, in particular, semions result to have special properties. An analogy with ultraviolet structures known in anyon quantum mechanics is drawn, and it is used to…
Quantum Calogero-Sutherland model of $A_n$ type is completely integrable. Using this fact, we give an elementary construction of lowering an raising operators for the trigonometric case. This is similar, but more complicated (due to the…