Higher-order Time-Symmetry-Breaking Phase Transition due to meeting of an Exceptional Point and Fano Resonance

TL;DR

This paper theoretically explores a higher-order time-symmetry-breaking phase transition caused by the interplay of an exceptional point and Fano resonance in a system of two discrete states coupled to a continuum, revealing complex decay dynamics.

Contribution

It introduces a theoretical framework for analyzing higher-order phase transitions driven by energy-dependent self-energy effects near a continuum threshold.

Findings

Identification of a higher-order phase transition due to energy dependence.

Demonstration of the competition between Van Hove singularity and Fano resonance.

Analysis of decay process dynamics near the continuum threshold.

Abstract

We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue prob- lem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy depen- dence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry breaking phase transition: as a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.