Quantum entanglement in inhomogeneous one-dimensional systems

Details

Supervisors

Walmsley Hagendorf, Christian

Faculty

Faculté des sciences

Degree label

Master [120] en sciences physiques, à finalité approfondie

Abstract

Entanglement is one of the most fundamental characteristics of quantum mechanics, yet one of the most intriguing. The interest in quantum entanglement started in the 1930s with the famous EPR paradox and has since found applications in various areas of physics. In this thesis, we study entanglement in the context of inhomogeneous one-dimensional systems. In particular, we focus on free-fermion models constructed from families of orthogonal polynomials. We investigate two entanglement measures, namely, the so-called entanglement entropy and the so-called bipartite fidelity. We first study these quantities in the ground state and first excited state of the so-called XX model, which we construct from the Chebyshev polynomials of the second kind. We then study an inhomogeneous model based on the Krawtchouk polynomials. We compare our numerical results with known conjectures for the entropy. For the bipartite fidelity, we give some conjectures based on numerical observations.