Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians

• URL: http://arxiv.org/abs/2003.03405v2
• Date: Tue, 11 Aug 2020 18:42:17 GMT
• Title: Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians
• Authors: Vincent P. Flynn, Emilio Cobanera, Lorenza Viola
• Abstract summary: We show that stability-to-instability transitions may be classified in terms of a suitably generalized $mathcalPmathcalT$ symmetry. We characterize the stability phase diagram of a bosonic analogue to the Kitaev-Majorana chain under a wide class of boundary conditions. Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically stable regime, whereby all observables undergo bounded evolution in time, and a dynamically unstable one, whereby evolution is unbounded for at least some observables. We show that stability-to-instability transitions may be classified in terms of a suitably generalized $\mathcal{P}\mathcal{T}$ symmetry, which can be broken when diagonalizability is lost at exceptional points in parameter space, but also when degenerate real eigenvalues split off the real axis while the system remains diagonalizable. By leveraging tools from Krein stability theory in indefinite inner-product spaces, we introduce an indicator of stability phase transitions, which naturally extends the notion of phase rigidity from non-Hermitian quantum mechanics to the bosonic setting. As a paradigmatic example, we fully characterize the stability phase diagram of a bosonic analogue to the Kitaev-Majorana chain under a wide class of boundary conditions. In particular, we establish a connection between phase-dependent transport properties and the onset of instability, and argue that stable regions in parameter space become of measure zero in the thermodynamic limit. Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.

Related papers

• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking [14.693424479293737]
  We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. We find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. We construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
  arXiv  Detail & Related papers  (2024-10-16T18:00:00Z)
• A little bit of self-correction [0.1437446768735628]
  We investigate the emergence of stable subspaces in the low-temperature quantum thermal dynamics of finite spin chains. The appearance of metastable subspaces is not directly related to the entanglement structure of the ground state(s) This work highlights that there can be non-trivial quantum behavior in the thermal dynamics of noncommuting many body models.
  arXiv  Detail & Related papers  (2024-08-27T11:22:38Z)
• Measurement-induced entanglement transition in chaotic quantum Ising chain [42.87502453001109]
  We study perturbations that break the integrability and/or the symmetry of the model, as well as modifications in the measurement protocol, characterizing the resulting chaos and lack of integrability through the Dissipative Spectral Form Factor (DSFF) We show that while the measurement-induced phase transition and its properties appear broadly insensitive to lack of integrability and breaking of the $bbZ$ symmetry, a modification of the measurement basis from the transverse to the longitudinal direction makes the phase transition disappear altogether.
  arXiv  Detail & Related papers  (2024-07-11T17:39:29Z)
• Defining stable phases of open quantum systems [0.0]
  We show that uniformity is satisfied in a canonical classical cellular automaton. We conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability.
  arXiv  Detail & Related papers  (2023-08-28T17:55:31Z)
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes [0.0]
  Exact solutions for non-Hermitian quantum many-body systems are rare but may provide valuable insights into the interplay between Hermitian and non-Hermitian components. We report our investigation of a non-Hermitian variant of a p-wave Kitaev chain by introducing staggered imbalanced pair creation and quench terms.
  arXiv  Detail & Related papers  (2023-04-30T14:41:42Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• 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)
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains [68.8204255655161]
  We show that even in the absence of disorder, and in the presence of bulk heating, $pi$ edge modes are long lived. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace.
  arXiv  Detail & Related papers  (2021-05-28T12:13:14Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Quotient symmetry protected topological phenomena [0.0]
  We show that topological phenomena can be stable over a large part of parameter space even when the bulk is strictly speaking in a trivial phase of matter. Although the Haldane phase is then adiabatically connected to a product state, we show that characteristic phenomena -- edge modes, entanglement degeneracies and bulk phase transitions -- remain parametrically stable.
  arXiv  Detail & Related papers  (2021-02-17T19:00:04Z)
• Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains [68.8204255655161]
  We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain. We establish a coherent self-feedback mechanism as the reservoir couples frequency-dependent to the spin chain.
  arXiv  Detail & Related papers  (2020-06-05T09:16:28Z)

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.