Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points

Purkayastha, Archak (2023) Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points. Physical Review Letters, 130 (18). p. 187101. ISSN 0031-9007

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Abstract

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

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IITH Creators:

IITH Creators	ORCiD
Purkayastha, Archak	http://www.orcid.org/0000-0002-6204-7280

Item Type:

Article

Uncontrolled Keywords:

Chemical potential; Bands edges; Exceptional points; Fermionic chains; One-dimensional; Quantum transport; Spectra's; Subdiffusive behavior; Symmetrics; System transport; Transfer matrixes; Phase transitions; Quantum chemistry; Transfer matrix method

Subjects:

Physics
Physics > Classical mechanics
Physics > Modern physics

Divisions:

Department of Physics

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

28 Sep 2023 12:48

Last Modified:

28 Sep 2023 12:48

URI:

http://raiithold.iith.ac.in/id/eprint/11719