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



Downloads per month over past year

Enciso, Alberto and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2008) A novel quasi-exactly solvable spin chain with nearest-neighbors interactions. Nuclear physics B, 789 (3). pp. 452-482. ISSN 0550-3213

[thumbnail of Finkel12.pdf]
Creative Commons Attribution.


Official URL: http://dx.doi.org/10.1016/j.nuclphysb.2007.07.001


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 Schrodinger 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.

Item Type:Article
Additional Information:

©2007 Elsevier B.V. All rights reserved.
This work was partially supported by the DGI under grant no. FIS2005-00752, and by the Complutense University and the DGUI under grant No. GR69/06-910556. A.E. acknowledges the financial support of the Spanish Ministry of Education and Science through an FPU scholarship. The authors would also like to thank V. Martín-Mayor for useful discussions on the moments method.

Uncontrolled Keywords:Spin chains; Quasi-exact solvability; Calogero–Sutherland models; Freezing trick
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31134
Deposited On:13 Jul 2015 18:10
Last Modified:10 Dec 2018 15:09

Origin of downloads

Repository Staff Only: item control page