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Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points.

Madhumita Saha1,2, Bijay Kumar Agarwalla1, Manas Kulkarni2

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We found a link between parity-time symmetry in optics and quantum transport in fermionic chains. This reveals subdiffusive transport and a quantum phase transition at band edges in open systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Non-Hermitian Physics

Background:

  • Parity-time (PT) symmetry is a concept from non-Hermitian physics, often studied in optical systems.
  • Quantum transport describes how particles move through a system, influenced by quantum mechanics.
  • One-dimensional (1D) fermionic chains are fundamental models in condensed matter physics.

Purpose of the Study:

  • To explore the connection between PT-symmetric optical systems and quantum transport in 1D fermionic chains.
  • To investigate the spectral properties and transport behavior of these systems in a two-terminal open setting.
  • To identify universal phenomena and phase transitions related to PT symmetry in quantum transport.

Main Methods:

  • Utilizing 2x2 transfer matrices to analyze the spectrum of 1D tight-binding chains with periodic potentials.
  • Identifying non-Hermitian symmetries analogous to PT symmetry in the transfer matrices.
  • Connecting exceptional points of the transfer matrix to band edges of the spectrum.
  • Analyzing quantum transport in a two-terminal setup with zero-temperature baths.

Main Results:

  • Non-Hermitian transfer matrices exhibit PT-like symmetry, leading to transitions at exceptional points.
  • Exceptional points of the unit cell transfer matrix correspond to the band edges of the spectrum.
  • Subdiffusive scaling of conductance (exponent 2) is observed when bath chemical potentials match band edges.
  • A dissipative quantum phase transition occurs as the chemical potential crosses band edges, analogous to mobility edge transitions.

Conclusions:

  • A deep connection exists between PT-symmetric optical systems and quantum transport in 1D fermionic chains.
  • The identified phenomena, including subdiffusive transport and dissipative phase transitions, are universal and independent of lattice details.
  • These transport properties and phase transitions are unique to open systems and absent in their closed counterparts.