Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble

• URL: http://arxiv.org/abs/2310.16693v1
• Date: Wed, 25 Oct 2023 15:04:03 GMT
• Title: Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Authors: Jos\'e Vinaixa, Bego\~na Mula, Alfredo Dea\~no, Silvia N. Santalla, Javier Rodr\'iguez-Laguna
• Abstract summary: We characterize the long-term state of the 1D Dirac vacuum stirred by an impenetrable object. For a slow motion, the effective Floquet Hamiltonian presents features typical of the Gaussian determinant ensemble. If the obstacle moves fast enough, the effective Floquet Hamiltonian presents a Poissonian behavior.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We characterize the long-term state of the 1D Dirac vacuum stirred by an impenetrable object, modeled as the ground state of a finite free-fermionic chain dynamically perturbed by a moving classical obstacle which suppresses the local hopping amplitudes. We find two different regimes, depending on the velocity of the obstacle. For a slow motion, the effective Floquet Hamiltonian presents features which are typical of the Gaussian orthogonal ensemble, and the occupation of the Floquet modes becomes roughly homogeneous. Moreover, the long term entanglement entropy of a contiguous block follows a Gaussian analogue of Page's law, i.e. a volumetric behavior. Indeed, the statistical properties of the reduced density matrices correspond to those of a random Slater determinant, which can be described using the Jacobi ensemble from random matrix theory. On the other hand, if the obstacle moves fast enough, the effective Floquet Hamiltonian presents a Poissonian behavior. The nature of the transition is clarified by the entanglement links, which determine the effective geometry underlying the entanglement structure, showing that the one-dimensionality of the physical Hamiltonian dissolves into a random adjacency matrix as we slow down the obstacle motion.

Related papers

• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Radiative transport in a periodic structure with band crossings [52.24960876753079]
  We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions. We consider both deterministic and random scenarios. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
  arXiv  Detail & Related papers  (2024-02-09T23:34:32Z)
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance [49.1574468325115]
  We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. We find that the dynamics of the spin ensemble now spans a more expansive effective Hilbert space.
  arXiv  Detail & Related papers  (2023-09-19T16:44:14Z)
• Spin relaxation dynamics with a continuous spin environment: the dissipaton equation of motion approach [11.335986457834348]
  We present the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. We derive the fluctuation-dissipation theorem (FDT) of the spin bath from a microscopic perspective. We envision this work provides new insights to extend the hierarchical equations of motion (HEOM) and DEOM approach to certain types of anharmonic enviroments.
  arXiv  Detail & Related papers  (2023-02-01T03:47:11Z)
• Symmetry-resolved entanglement in a long-range free-fermion chain [0.0]
  We study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain. We find entanglement, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.
  arXiv  Detail & Related papers  (2022-02-11T19:38:38Z)
• Pattern formation in one-dimensional polaron systems and temporal orthogonality catastrophe [0.0]
  Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. We employ the so-called Gross Ansatz approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron.
  arXiv  Detail & Related papers  (2021-10-21T14:20:12Z)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• 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)
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces [0.0]
  Integrable Floquet spin chains are known to host strong zero and $pi$ modes which are boundary operators respectively commute and anticommute. Weak interactions modify the strong modes to almost strong modes that almost commute or anticommute with the Floquet unitary. The effective single particle models in the Krylov subspace are discussed, and the properties of the Krylov chain that ensure stable $0$ and $pi$ modes are highlighted.
  arXiv  Detail & Related papers  (2021-05-27T15:43:34Z)
• Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors [0.0]
  We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian.
  arXiv  Detail & Related papers  (2021-02-15T22:29:01Z)

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.