Integrble Models in Condensed Matter Physics

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.

Talk presented at NATO Gran Finale Conference, Como, Italy, September 1993

Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some integrable spin models and their relevance in the study of real systems. The emphasis in the review is on physical understanding rather than on the mathematical aspects of integrability.

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves in terms of corresponding integrable models.

Talk presented by the second author at the Inaugural Coference of the Asia Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this note is to give a resume of the Seiberg-Witten theory in the simplest possible mathematical terms.

Lecture notes delivered in Barcellona in the fall of 2003

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns itself mainly with correlations between results in classical hierarchies and quantum lattice models. The second part, consisting of chapters 4-6, deals almost entirely with deriving results concerned with quantum lattice models.

Talks given at the workshop ``Frontiers in Quantum Field Theory'', held in Urumqi, Xinjiang Uygur Autonomous Region, People's Republic of China, 11-19 August 1996.

An overview of the quantum integrable systems (QIS) is presented. Basic concepts of the theory are highlighted stressing on the unifying algebraic properties, which not only helps to generate systematically the representative Lax operators of different models, but also solves the related eigenvalue problem in an almost model independent way. Difference between the approaches in the integrable ultralocal and nonultralocal quantum models are explained and the interrelation betw...

Some additional references are included on the last 3 pages.