Critically slow Hilbert-space ergodicity in quantum morphic drives

• URL: http://arxiv.org/abs/2502.06936v1
• Date: Mon, 10 Feb 2025 19:00:00 GMT
• Title: Critically slow Hilbert-space ergodicity in quantum morphic drives
• Authors: Saúl Pilatowsky-Cameo, Soonwon Choi, Wen Wei Ho,
• Abstract summary: We prove that the Thue-Morse drive achieves a very strong notion of quantum ergodicity in the long-time limit.<n>On the other hand, we find the dynamics also approximates a Floquet drive for arbitrarily long albeit finite periods of time.<n>Our work presents a new class of dynamics in time-dependent quantum systems where full ergodicity is eventually attained.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The maximum entropy principle is foundational for statistical analyses of complex dynamics. This principle has been challenged by the findings of a previous work [Phys. Rev. X 7, 031034 (2017)], where it was argued that a quantum system driven in time by a certain aperiodic sequence without any explicit symmetries, dubbed the Thue-Morse drive, gives rise to emergent nonergodic steady states which are underpinned by effective conserved quantities. Here, we resolve this apparent tension. We rigorously prove that the Thue-Morse drive achieves a very strong notion of quantum ergodicity in the long-time limit: the time evolution of any initial state uniformly visits every corner of its Hilbert space. On the other hand, we find the dynamics also approximates a Floquet drive for arbitrarily long albeit finite periods of time with no characteristic timescale, resulting in a scale-free ergodic dynamics we call critically slow complete Hilbert-space ergodicity (CS-CHSE). Furthermore, numerical studies reveal that CS-CHSE is not specific to the Thue-Morse drive and is in fact exhibited by many other aperiodic drives derived from morphic sequences, i.e., words derived from repeatedly applying substitution rules on basic characters. Our work presents a new class of dynamics in time-dependent quantum systems where full ergodicity is eventually attained, but only after astronomically long times.

Related papers

• Probing quantum many-body dynamics using subsystem Loschmidt echos [39.34101719951107]
  We experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo.<n>In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations.<n>In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit.
  arXiv  Detail & Related papers  (2025-01-28T14:51:37Z)
• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.<n>We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.<n>Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Exploring Hilbert-Space Fragmentation on a Superconducting Processor [23.39066473461786]
  Isolated interacting quantum systems generally thermalize, yet there are several counterexamples for the breakdown of ergodicity. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. Here, we experimentally explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits.
  arXiv  Detail & Related papers  (2024-03-14T04:39:14Z)
• Hilbert-Space Ergodicity in Driven Quantum Systems: Obstructions and Designs [0.0]
  We study a notion of quantum ergodicity for closed systems with time-dependent Hamiltonians.<n>We show that statistical pseudo-randomness can already be achieved by a quantum system driven with a single frequency.
  arXiv  Detail & Related papers  (2024-02-09T19:00:00Z)
• Long-lived topological time-crystalline order on a quantum processor [16.781279220543517]
  Topologically ordered phases of matter elude Landau's symmetry-breaking theory. We report the observation of signatures of such a phenomenon with programmable superconducting qubits arranged on a square lattice. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy.
  arXiv  Detail & Related papers  (2024-01-09T03:20:15Z)
• Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives [0.0]
  We investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.
  arXiv  Detail & Related papers  (2023-06-20T18:00:01Z)
• Exact universal bounds on quantum dynamics and fast scrambling [0.0]
  We show that the spectral form factor sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times. We use this result to constrain the scrambling of information in interacting many-body systems.
  arXiv  Detail & Related papers  (2022-12-28T18:47:20Z)
• Slow dynamics and non-ergodicity of the bosonic quantum East model in the semiclassical limit [0.0]
  We study the unitary dynamics of the bosonic quantum East model. We consider the semiclassical limit of large (but finite) site occupancy. We characterize states which are non-ergodic on all timescales in the otherwise ergodic regime.
  arXiv  Detail & Related papers  (2022-09-14T22:31:25Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• The role of fluctuations in quantum and classical time crystals [58.720142291102135]
  We study the role of fluctuations on the stability of the system and find no distinction between quantum and classical DTCs. This allows us to probe the fluctuations in an experiment using two strongly coupled parametric resonators subject to classical noise.
  arXiv  Detail & Related papers  (2022-03-10T19:00:01Z)
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
  Quantum-body systems display rich phase structure in their low-temperature equilibrium states. We experimentally observe an eigenstate-ordered DTC on superconducting qubits. Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems [0.0]
  We derive rigorous, non-perturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasi-periodic driving. Our bound for Thue-Morse quasi-periodic driving suggests that the heating time scales like $(omega/g)-Cln(omega/g)$ with a positive constant $C$ and a typical energy scale $g$ of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-01-18T13:22:54Z)
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays [41.74498230885008]
  We experimentally investigate non-equilibrium dynamics following rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. We discover that scar revivals can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order.
  arXiv  Detail & Related papers  (2020-12-22T19:00:02Z)

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.