Universal subdiffusive behavior at band edges from transfer matrix
exceptional points
- URL: http://arxiv.org/abs/2205.02214v2
- Date: Fri, 12 May 2023 09:13:36 GMT
- Title: Universal subdiffusive behavior at band edges from transfer matrix
exceptional points
- Authors: Madhumita Saha, Bijay Kumar Agarwalla, Manas Kulkarni, Archak
Purkayastha
- Abstract summary: We find a connection between symmetric optical systems and quantum transport in one-dimensional fermionic chains.
We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum.
We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We discover a deep connection between parity-time (PT) 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 $2 \times 2$ transfer matrices. We find that these non-Hermitian
matrices have a symmetry exactly analogous to the PT-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.
Related papers
- Flux-Tunable Regimes and Supersymmetry in Twisted Cuprate Heterostructures [39.58317527488534]
Two Josephson junctions are integrated in a SQuID circuit threaded by a magnetic flux.
We show that the flowermon qubit regime is maintained up to a finite critical value of the magnetic field.
The interplay between the inherent twisted d-wave nature of the order parameter and the external magnetic flux enables the implementation of different artificial atoms.
arXiv Detail & Related papers (2024-05-06T13:27:19Z) - Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement.
We show that the passage to the monitored universality occurs abruptly at finite partial post-selection.
Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
arXiv Detail & Related papers (2023-12-21T16:53:42Z) - Entanglement phase transition due to reciprocity breaking without
measurement or post-selection [59.63862802533879]
EPT occurs for a system undergoing purely unitary evolution.
We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
arXiv Detail & Related papers (2023-08-28T14:28:59Z) - Emergence of non-Abelian SU(2) invariance in Abelian frustrated
fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette.
Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry.
At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z) - Parity-dependent unidirectional and chiral photon transfer in
reversed-dissipation cavity optomechanics [11.712867508048555]
We show broadband nonreciprocal photon transmission in the emphreversed-dissipation regime.
In the reversed-dissipation regime, the nonreciprocal bandwidth is no longer limited by the mechanical mode linewidth.
We find that the direction of the unidirectional and chiral energy transfer could be reversed by changing the emphparity of the Eps.
arXiv Detail & Related papers (2022-12-22T23:57:00Z) - Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity.
This enables an exact description of the full dynamics and dissipative spectrum.
Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
arXiv Detail & Related papers (2021-09-27T17:45:42Z) - Fall-to-the-centre as a $\mathcal{PT}$ symmetry breaking transition [0.0]
Inverse square potential arises in a number of physical problems.
The transition at this critical potential strength can be regarded as an example of a $mathcalPT$ symmetry breaking transition.
arXiv Detail & Related papers (2021-07-04T00:15:36Z) - SYK meets non-Hermiticity II: measurement-induced phase transition [16.533265279392772]
We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space.
We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.
arXiv Detail & Related papers (2021-04-16T17:55:08Z) - Signatures of a critical point in the many-body localization transition [0.0]
We show a possible finite-size precursor of a critical point that shows a typical finite-size scaling.
We show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide.
arXiv Detail & Related papers (2020-10-17T10:33:13Z) - SUSY shields the scaling symmetry of conformal quantum mechanics [0.0]
In a strongly attractive potential, the scaling symmetry is broken to a discrete subgroup while, in a strongly repulsive potential, it is preserved at quantum level.
We show that potentials with couplings in the strongly-repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry.
arXiv Detail & Related papers (2019-12-30T17:15:51Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.