One of the main features of statistical systems out of equilibrium is the currents they exhibit in
their stationary state: microscopic currents of probability between configurations, which …

The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to
characterize the spectral problem of the Heisenberg XXZ spin-1 2 chain on the segment with …

In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with
the XXZ spin-1 2 chain on the segment with two generic integrable boundaries acting on the …

This chapter describes a general scheme for constructing quantum integrable models within
the Quantum Inverse Scattering Method (QISM) framework. Much of what is described here …

A bstract We show that the scalar products of on-shell and off-shell Bethe vectors in the
algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find …

We investigate special solutions to the Bethe Ansatz equations (BAE) for open integrable
XXZ Heisenberg spin chains containing phantom (infinite) Bethe roots. The phantom Bethe …

We construct the coordinate Bethe ansatz for all eigenstates of the open spin-1 2 XXZ chain
that fulfill the phantom roots criterion (PRC). Under the PRC, the Hilbert space splits into two …

A bstract We introduce new\({U} _ {\mathfrak {q}}{\mathfrak {sl}} _2\)-invariant boundary
conditions for the open XXZ spin chain. For generic values of\(\mathfrak {q}\) we couple the …

Abstract An operator of Heun-Askey-Wilson type is diagonalized within the framework of the
algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and …

We apply our new approach of quantum Separation of Variables (SoV) to the complete
characterization of the transfer matrix spectrum of quantum integrable lattice models …