2019/07/17 by Ananya Ghatak, Ghatak, Ananya, Tanmoy Das +1
Chemistry · Physics and Astronomy · #FOS: Physical sciences #Mechanical and Optical Resonators #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Molecular spectroscopy and chirality #Quantum Gases (cond-mat.quant-gas) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1907.07333
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian quantum theory is envisioned to have far-reaching implications in basic science and applications. It is known that the PT-inner product is defined with respect to a non-canonical, system-generated dynamical symmetry, namely the C symmetry. Here, we show that the PT invariant equation of motion is defined by the simultaneous time evolution of the state ψ(t) and the operator C(t) to manifest unitarity. The dynamical C operator lends itself to a new term in the Berry phase. The PT symmetric theory is not generally applicable for spin-1/2 fermions, since here PT inner product vanishes due to Kramer's degeneracy. We consider a spin-1/2 non-Hermitian setup which acquires the combined (PT)2=+1 symmetry, despite T2=-1 and P2=+1. The Hamiltonian inherits a non-Abelian adiabatic transporter and the topological degeneracy via the combined evolution of the ψ(t) state and the C(t) operator. The putative dynamical C symmetry can be a novel springboard for many other exotic quantum and topological phases.