arXiv subjects

Alexander Garbali

Publications and source records attributed to Alexander Garbali.

2 recordsLinked to original sources

arXiv2018

The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

We study the domain wall partition function $Z_N$ for the $U_q(A_2^{(2)})$ (Izergin-Korepin) integrable $19$-vertex model on a square lattice of size $N$. $Z_N$ is a symmetric function of two sets of parameters: horizontal $ζ_1,..,ζ_N$ and vertical $z_1,..,z_N$ rapidities. For generic values of the parameter $q$ we derive the recurrence relation for the domain wall partition function relating $Z_{N+1}$ to $P_N Z_N$, where $P_N$ is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables $ζ_1,..,ζ_N$ and $z_1,..,z_N$. After setting $q^3=-1$ the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by $P_N$.

math-ph↗

arXiv2014

The scalar product of XXZ spin chain revisited. Application to the ground state at $Δ=-1/2$

For the scalar product $S_n$ of the XXZ $s=1/2$ spin chain we derive a new determinant expression which is symmetric in the Bethe roots. We consider an application of this formula to the inhomogeneous groundstate of the model with $Δ=-1/2$ with twisted periodic boundary conditions. At this point the ground state eigenvalue $τ_n$ of the transfer matrix is known and has a simple form that does not contain the Bethe roots. We use the knowledge of $τ_n(μ)$ to obtain a closed expression for the scalar product. The result is written in terms of Schur functions. The computations of the normalization of the ground state and the expectation value of $σ^z$ are also presented.

math-ph↗