Transition from degeneracy to coalescence: theorem and applications

• URL: http://arxiv.org/abs/2107.13185v1
• Date: Wed, 28 Jul 2021 06:26:21 GMT
• Title: Transition from degeneracy to coalescence: theorem and applications
• Authors: P. Wang, K. L. Zhang, and Z. Song
• Abstract summary: We present a theorem on the existence of transition between DP and EP for a general system. The obtained EP is robust to the strength of non-Hermitian terms. This finding reveals the ubiquitous connection between DP and EP.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exceptional point (EP) is exclusive for non-Hermitian system and distinct from that at a degeneracy point (DP), supporting intriguing dynamics, which can be utilized to probe quantum phase transition and prepare eigenstates in a Hermitian many-body system. In this work, we investigate the transition from DP for a Hermitian system to EP driven by non-Hermitian terms. We present a theorem on the existence of transition between DP and EP for a general system. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional model, which allows the existence of transition between fully degeneracy and exceptional spectra driven by non-Hermitian tunnelings in real and k spaces, respectively. We also study the EP dynamics for generating coalescing edge modes in Su-Schrieffer-Heeger-like models. This finding reveals the ubiquitous connection between DP and EP.

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