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A. Enciso

Publications and source records attributed to A. Enciso.

10 recordsLinked to original sources
arXiv2012

Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models

We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A_{N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for thezero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models.

cond-mat.stat-mech↗
arXiv2010

On the level density of spin chains of Haldane--Shastry type

We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the dispersion relation.

math-ph↗
arXiv2009

Spin chains of Haldane-Shastry type and a generalized central limit theorem

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a nontrivial modification of the classical central limit theorem, and is especially suited to models whose partition function is explicitly known. In particular, we provide the first theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.

math-ph↗
arXiv2007

Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.

nlin.SI↗
arXiv2007

A novel quasi-exactly solvable spin chain with nearest-neighbors interactions

In this paper we study a novel spin chain with nearest-neighbors interactions depending on the sites coordinates, which in some sense is intermediate between the Heisenberg chain and the spin chains of Haldane-Shastry type. We show that when the number of spins is sufficiently large both the density of sites and the strength of the interaction between consecutive spins follow the Gaussian law. We develop an extension of the standard freezing trick argument that enables us to exactly compute a certain number of eigenvalues and their corresponding eigenfunctions. The eigenvalues thus computed are all integers, and in fact our numerical studies evidence that these are the only integer eigenvalues of the chain under consideration. This fact suggests that this chain can be regarded as a finite-dimensional analog of the class of quasi-exactly solvable Schroedinger operators, which has been extensively studied in the last two decades. We have applied the method of moments to study some statistical properties of the chain's spectrum, showing in particular that the density of eigenvalues follows a Wigner-like law. Finally, we emphasize that, unlike the original freezing trick, the extension thereof developed in this paper can be applied to spin chains whose associated dynamical spin model is only quasi-exactly solvable.

hep-th↗
arXiv2006

Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.

nlin.SI↗
arXiv2004

Haldane-Shastry spin chains of BC_N type

We introduce four types of SU(2M+1) spin chains which can be regarded as the BC_N versions of the celebrated Haldane-Shastry chain. These chains depend on two free parameters and, unlike the original Haldane-Shastry chain, their sites need not be equally spaced. We prove that all four chains are solvable by deriving an exact expression for their partition function using Polychronakos's "freezing trick". From this expression we deduce several properties of the spectrum, and advance a number of conjectures that hold for a wide range of values of the spin M and the number of particles. In particular, we conjecture that the level density is Gaussian, and provide a heuristic derivation of general formulas for the mean and the standard deviation of the energy.

hep-th↗
arXiv2004

Solvable scalar and spin models with near-neighbors interactions

We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the corresponding eigenfunctions are explicitly computed. We also study the scalar reductions of the models, some of which had already appeared in the literature, and compute their algebraic eigenfunctions in closed form. In the rational cases, for which only partial results were available, we give concise expressions of the eigenfunctions in terms of generalized Laguerre and Jacobi polynomials.

hep-th↗
arXiv2004

On quantum integrability and Hamiltonians with pure point spectrum

We prove that any $n$-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set $Σ\subset\mathbb R$ there exists an integrable $n$-dimensional Hamiltonian which realizes it as its spectrum. We develop several applications of these results and discuss their implications in the general framework of quantum integrability.

math-ph↗