Topological classifications of quadratic bosonic excitations in closed and open systems with examples

• URL: http://arxiv.org/abs/2103.15200v5
• Date: Tue, 11 Jan 2022 20:54:18 GMT
• Title: Topological classifications of quadratic bosonic excitations in closed and open systems with examples
• Authors: Yan He and Chih-Chun Chien
• Abstract summary: We present a 1D bosonic Su-Schrieffer-Heeger model with chiral symmetry and a 2D bosonic topological insulator with time-reversal symmetry to show the corresponding open systems may fall into different classes.
• Score: 1.788349916009287
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The topological classifications of quadratic bosonic systems according to the symmetries of the dynamic matrices from the equations of motion of closed systems and the effective Hamiltonians from the Lindblad equations of open systems are analyzed. While the non-Hermitian dynamic matrix and effective Hamiltonian both lead to a ten-fold way table, the system-reservoir coupling may cause a system with or without coupling to a reservoir to fall into different classes. A 2D Chern insulator is shown to be insensitive to the different classifications. In contrast, we present a 1D bosonic Su-Schrieffer-Heeger model with chiral symmetry and a 2D bosonic topological insulator with time-reversal symmetry to show the corresponding open systems may fall into different classes.

Related papers

• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous [62.997667081978825]
  The impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom. The dynamics of this system is determined in closed analytical form. We observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior.
  arXiv  Detail & Related papers  (2021-11-23T20:25:57Z)
• 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)
• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries [0.0]
  subsystem symmetries are associated to conserved magnetization along rows and columns of a square lattice. We show that subsystem symmetries alone cannot account for such a number of inert states, even with infinite-range interactions.
  arXiv  Detail & Related papers  (2021-07-20T18:00:49Z)
• Quantum information dynamics in a high-dimensional parity-time-symmetric system [3.2363688674314814]
  Non-Hermitian systems with parity-time ($mathcalPT$) symmetry give rise to exceptional points (EPs) with exceptional properties. We simulate quantum dynamics of a four-dimensional $mathcalPT$-symmetric system across a fourth-order exceptional point.
  arXiv  Detail & Related papers  (2021-02-12T19:00:44Z)
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems [0.0]
  We provide a rigorous construction of Markovian master equations for a wide class of quantum systems. We show that, for non-degenerate systems under a full secular approximation, the effective Lindblad operators are the normal modes of the system. We also address the particle and energy current flowing through the system in a minimal two-bath scheme and find that they hold the structure of Landauer's formula.
  arXiv  Detail & Related papers  (2021-01-22T19:25:17Z)
• Subsystem symmetry enriched topological order in three dimensions [0.0]
  We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. We study the non-trivial action of the symmetries on boundary of this model, uncovering a mixed boundary anomaly between global and subsystem symmetries.
  arXiv  Detail & Related papers  (2020-04-08T18:01:06Z)
• 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.