Boundary time crystals in collective $d$-level systems

• URL: http://arxiv.org/abs/2102.03374v2
• Date: Wed, 14 Apr 2021 19:45:40 GMT
• Title: Boundary time crystals in collective $d$-level systems
• Authors: Luis Fernando dos Prazeres, Leonardo da Silva Souza, Fernando Iemini
• Abstract summary: Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
• Score: 64.76138964691705
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Boundary time crystals (BTC's) are non-equilibrium phases of matter occurring in quantum systems in contact to an environment, for which a macroscopic fraction of the many body system breaks time translation symmetry. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$. We find that BTC's appear in different forms for the different cases. We first consider the model with collective $d=2$-level systems [presented in Phys. Rev. Lett. $121$, $035301$ ($2018$)], whose dynamics is described by a Lindblad master equation, and perform a throughout analysis of its phase diagram and Jacobian stability for different interacting terms in the coherent Hamiltonian. In particular, using perturbation theory for general (non Hermitian) matrices we obtain analytically how a specific $\mathbb{Z}_2$ symmetry breaking Hamiltonian term destroys the BTC phase in the model. Based on these results we define a $d=4$ model composed of a pair of collective $2$-level systems interacting with each other. We show that this model support richer dynamical phases, ranging from limit-cycles, period-doubling bifurcations and a route to chaotic dynamics. The BTC phase is more robust in this case, not annihilated by the former symmetry breaking Hamiltonian terms. The model with collective $d=3$-level systems is defined similarly, as competing pairs of levels, but sharing a common collective level. The dynamics can deviate significantly from the previous cases, supporting phases with the coexistence of multiple limit-cycles, closed orbits and a full degeneracy of zero Lyapunov exponents.

Related papers

• A comparison between classical and Bohmian quantum chaos [0.0]
  We study the emergence of chaos in a 2d system corresponding to a classical Hamiltonian system $V= frac12(omega_x2x2+omega_y2y2)+epsilon xy2$.
  arXiv  Detail & Related papers  (2024-09-18T15:30:36Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Quantum chaos in PT symmetric quantum systems [2.2530496464901106]
  We study the interplay between $mathcalPT$-symmetry and quantum chaos in a non-Hermitian dynamical system. We find that the complex level spacing ratio can distinguish between all three phases. In the phases with $mathcalPT$-symmetry, the OTOC exhibits behaviour akin to what is observed in the Hermitian system.
  arXiv  Detail & Related papers  (2024-01-14T06:47:59Z)
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics [5.117091825006161]
  We analyze the degeneracy dependence on the size of two-level boson models with a $u(n+1)$ dynamical algebra. We show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with $n=1$, but in systems with $n>1$, this average only works as an order parameter in the mean-field limit.
  arXiv  Detail & Related papers  (2023-03-29T09:20:29Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
  We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC) We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
  arXiv  Detail & Related papers  (2021-12-21T20:25:02Z)
• Symmetries and conserved quantities of boundary time crystals in generalized spin models [0.0]
  We investigate how symmetries and conserved quantities relate to the occurrence of the boundary time crystal phase in a generalized spin model with Lindblad dissipation. Our results suggest that these two elements may be general requirements for the observation of a stable BTC phase relating symmetries and conserved quantities in arbitrary spin models.
  arXiv  Detail & Related papers  (2021-01-14T16:36:08Z)
• 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)
• Quantum correlations in $\mathcal{PT}$-symmetric systems [0.0]
  We study the dynamics of correlations in a paradigmatic setup to observe $mathcalPT$-symmetric physics. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely.
  arXiv  Detail & Related papers  (2020-02-25T19:00:02Z)

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.