This project aims to investigate the XYZ spin ½ chain, to extract new properties of this model, through its exact analytical solution. It captures the most generic, anisotropic, magnetic interaction in a one-dimensional system and it constitutes a reference system to better understand quantum magnetism and related phenomena. Starting from this spin chain, defined on a discrete lattice, we will study its odd number of sites sector to analyze frustration (i.e. imposing frustrated boundary conditions) and its implications. This sector allows investigating a part of the model’s Hilbert space usually inaccessible and largely overlooked in the past, which has been recently shown to host different properties compared to the even number of sites case. The standard Bethe ansatz procedure cannot be applied to the XYZ chain with an odd number of sites. Thus, our solution relies on the recent developments of Bethe ansatz techniques, namely the “off-diagonal” Bethe ansatz. This method starts from the TQ relations, which concern the Transfer matrix of the eight-vertex model. These identities are then generalized to the odd N case introducing an inhomogeneous term, and they lead to Bethe equations whose solutions identify the eigenstates of the system. So, it is possible to recover the energy spectrum of the Hamiltonian and compare it to exact diagonalization numerical results. Then, in the continuum limit, the XYZ chain maps in the famous sine-Gordon model, but this mapping is non-trivial. Studying the frustrated boundary condition sector of the chain will allow examining the field theory model, especially the behavior of topological excitations, known for their robustness. The treatment will then focus on out-of-equilibrium settings, which are important also for applications, such as quantum information and technologies.
The seminar will be chaired by Tim Verhagen, Department of Dielectrics.