Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models

• URL: http://arxiv.org/abs/2203.00247v2
• Date: Fri, 10 Jun 2022 00:33:30 GMT
• Title: Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Authors: Ken Mochizuki, Tomoki Ozawa
• Abstract summary: We show that imaginary scalar potentials do not open band gaps but lead to the formation of exceptional points. The imaginary vector potentials hinder the separation of low energy bands because of the lifting of degeneracy in the free system. We reproduce the dispersion relations of the continuum model when the complex scalar potential is sufficiently large.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore band structures of one-dimensional open systems described by periodic non-Hermitian operators, based on continuum models and tight-binding models. We show that imaginary scalar potentials do not open band gaps but instead lead to the formation of exceptional points as long as the strength of the potential exceeds a threshold value, which is contrast to closed systems where real potentials open a gap with infinitesimally small strength. The imaginary vector potentials hinder the separation of low energy bands because of the lifting of degeneracy in the free system. In addition, we construct tight-binding models through bi-orthogonal Wannier functions based on Bloch wavefunctions of the non-Hermitian operator and its Hermitian conjugate. We show that the bi-orthogonal tight-binding model well reproduces the dispersion relations of the continuum model when the complex scalar potential is sufficiently large.

Related papers

• Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice [0.0]
  Driven-dissipative light-matter systems can exhibit collective nonequilibrium phenomena due to loss and gain processes. We numerically predict a diverse range of stationary and non-stationary states resulting from the interplay of the tilt, tunneling, on-site interactions and loss and gain processes.
  arXiv  Detail & Related papers  (2024-04-29T12:28:52Z)
• Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems [0.0]
  We introduce a class of time-dependent non-Hermitian Hamiltonians that can describe a two-level system with temporally modulated on-site potential and couplings. Our proposed class of Hamiltonians can be employed in different platforms such as electronic circuits, acoustics, and photonics to design structures with hidden PT-symmetry.
  arXiv  Detail & Related papers  (2023-02-02T04:57:13Z)
• Continuum of Bound States in a Non-Hermitian Model [6.229083355999047]
  In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum. We show how this principle fails for non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential. We present experimentally-realizable 1D and 2D lattice models that can be used to study CLMs.
  arXiv  Detail & Related papers  (2022-10-06T08:09:42Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak [0.0]
  We introduce and explore an interacting cellular automaton that lies outside the existing classification of such automata. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. We analytically construct an extensive set of operators that anticommute with the time-evolution operator.
  arXiv  Detail & Related papers  (2022-05-17T18:00:00Z)
• 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)
• Self-consistent theory of mobility edges in quasiperiodic chains [62.997667081978825]
  We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-Andr'e-Harper model.
  arXiv  Detail & Related papers  (2020-12-02T19:00:09Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Localization of Rung Pairs in Hard-core Bose-Hubbard Ladder [13.46516066673]
  We study the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. In the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Our results reveal another interesting type of disorder-free localization related to a zero-energy flat band.
  arXiv  Detail & Related papers  (2020-05-18T08:40:40Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.