A bstract The Motzkin spin chain is a spin-1 frustration-free model introduced by Shor &
Movassagh. The ground state is constructed by mapping random walks on the upper half of …

Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A 2 n (2), A
2 n− 1 (2), B n (1), C n (1), D n (1)) and suitable corresponding K-matrices, we construct …

We consider quantum spins with S ≥ 1 S≥ 1, and two-body interactions with O (2S+ 1) O (2
S+ 1) symmetry. We discuss the ground state phase diagram of the one-dimensional system …

The Motzkin spin chain is a spin-$1 $ frustration-free model introduced by Shor &
Movassagh. The ground state is constructed by mapping random walks on the upper half of …

We study the family of spin-S quantum spin chains with a nearest neighbor interaction given
by the negative of the singlet projection operator. Using a random loop representation of the …

We study Slavnov's inner products for open Temperley-Lieb chains and their relations with
the KP hierarchy. We show that when s= 1/2 the quantum group invariant XXZ spin chain …

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1
Temperley–Lieb open quantum chain with “free” boundary conditions. We exploit the …

With the ionic Hubbard model (IHM) in mind, we construct a non-trivial generalization of the
Bethe ansatz (BA) wave function which naturally generalizes the Lieb–Wu wave function …

The simulation of interacting quantum matter remains challenging. The Hilbert space
dimension required to describe the physics grows exponentially with the system size, yet …

In this thesis we study a range of quantum spin systems and several related probabilistic
models on graphs. This includes classical spin systems such as the Ising model, the Potts …