Non-Hermitian operators in many-body physics

          @misc{ scivideos_PIRSA:24090178,
            doi = {},
            url = {https://pirsa.org/24090178},
            author = {Barnett, Jacob},
            keywords = {Quantum Matter},
            language = {en},
            title = {Non-Hermitian operators in many-body physics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {sep},
            note = {PIRSA:24090178 see, \url{https://scivideos.org/index.php/pirsa/24090178}}
          }
          

Abstract

Non-Hermitian Hamiltonians are a compulsory aspect of the linear dynamical systems that model many physical phenomena, such as those in electrical circuits, open quantum systems, and optics. Additionally, a representation of the quantum theory of closed systems with non-Hermitian observables possessing unbroken PT-symmetry is well-defined.   In this talk, I will second-quantize non-Hermitian quantum theories with paraFermionic statistics. To do this, I will introduce an efficient method to find conserved quantities when the Hamiltonian is free or translationally invariant. Using a specific non-Hermitian perturbation of the Su-Schrieffer-Heeger (SSH ) model, a prototypical topological insulator, I examine how PT-symmetry breaking occurs at the topological phase transition. Finally, I show that although finite-dimensional PT-symmetric quantum theories generalize the tensor product model of locality, they never permit Bell inequality violations beyond what is possible in the Hermitian quantum tensor product model.