arXiv subjects

M Zuparic

Publications and source records attributed to M Zuparic.

5 recordsLinked to original sources

arXiv2012

Studies in Integrable Quantum Lattice Models and Classical Hierarchies

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.

math-ph↗

arXiv2009

XXZ scalar products and KP

Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.

math-ph↗

arXiv2009

Domain wall partition functions and KP

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).

math-ph↗

arXiv2008

On free fermions and plane partitions

We use free fermion methods to re-derive a result of Okounkov and Reshetikhin relating charged fermions to random plane partitions, and to extend it to relate neutral fermions to strict plane partitions.

math-ph↗

arXiv2007

On the trigonometric Felderhof model with domain wall boundary conditions

We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda tau function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.

math-ph↗