PT-Symmetry Breaking Transitions in Polymeric Systems

TL;DR

This paper explores PT-symmetry breaking transitions in polymeric systems, linking DNA unzipping and quantum localization phenomena through non-Hermitian Hamiltonian models, revealing phase transitions in both continuum and lattice frameworks.

Contribution

It demonstrates the connection between DNA unzipping and PT-symmetry breaking in non-Hermitian models, extending understanding to discrete lattice systems with disorder.

Findings

Discrete models exhibit phase transitions from PT unbroken to broken phases.

PT transition points align with localization-delocalization transitions.

Results apply to both continuum and lattice polymer models.

Abstract

We show that classical DNA unzipping transition which is equivalently described by quantum mechanical localization-delocalization transition in the ground state of non-Hermitian single impurity Hatano-Nelson Hamiltonian is underpinned by generalized parity ({\bf P})-time reversal ({\bf T}) symmetry breaking transition. We also study the one-dimensional discretized version of Hatano-Nelson model in the presence of the single impurity and random disorder on a finite-size lattice. These discrete models are useful to study unzipping of a single adsorbed polymer from a surface. Our results show that the discrete models also undergo a phase transition from a PT unbroken phase to a broken phase. Interestingly, the generalized PT phase transition points coincide with the localization-delocalization transition for continuum as well as lattice models.