City Research Online

Abstract

In this thesis, we investigate the interplay between entanglement and internal symmetries in 1+1D quantum field theories (QFTs). Although the notion of symmetry-resolved entanglement has been widely studied in various systems, its behavior in excited states of massive QFTs remains largely unexplored. In the first part of the thesis, we focus on theories with global U(1) symmetry and compute the symmetry-resolved entanglement entropy and logarithmic negativity of zero-density excited states of the massive free complex boson and Dirac fermion. We find that the excess of symmetry-resolved entropy (and negativity) of these states with respect to the ground state is largely independent on the details of the excited state and it has a very simple dependence on the U(1) charge. We test our results numerically on a one-dimensional Fermi gas and on a one-dimensional harmonic chain, and we propose an interpretation of our formulae in terms of simple multi-qubit states. Next, we generalise the field-theoretic computation of symmetry-resolved entanglement measures to higher-dimensional, non-integrable field theories using semi-local twist operators, which are defined through their commutation relations with an algebra of local observables in a QFT. In the second part of the thesis, we turn our attention to the one-dimensional massive Ising QFT, which possesses a Z₂ symmetry. The ground state in the paramagnetic (disordered) phase of the theory is symmetric, and its Z₂-resolved entanglement entropy can be obtained from a two-point function of composite twist fields. We provide an exact expression for the cumulant expansion of this two-point function. In contrast, the ferromagnetic (ordered) phase features two Z₂-breaking vacua. The extent to which the symmetry is broken can be quantified by a relative entropy measure known as entanglement asymmetry. By making use of twist operators, we develop a method to compute entanglement asymmetry in massive 1+1D QFTs with discrete internal symmetry and apply this approach to the Ising model.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

Export

Downloads