Structural Stability Hypothesis of Dual Unitary Quantum Chaos

• URL: http://arxiv.org/abs/2402.19096v2
• Date: Tue, 27 Aug 2024 10:47:19 GMT
• Title: Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Authors: Jonathon Riddell, Curt von Keyserlingk, Tomaž Prosen, Bruno Bertini,
• Abstract summary: spectral correlations over small enough energy scales are described by random matrix theory. We consider fate of this property when moving from dual-unitary to generic quantum circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions.

Related papers

• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor [0.0]
  Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. We study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-07-29T12:02:24Z)
• Tensor product random matrix theory [39.58317527488534]
  We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
  arXiv  Detail & Related papers  (2024-04-16T21:40:57Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model [0.0]
  We show that the randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions in single-particle systems is lifted into many-body space. We then identify the universality of both the cross-correlations and the Gaussian distribution of expansion coefficients as the signatures of chaotic eigenstates.
  arXiv  Detail & Related papers  (2024-03-15T09:26:17Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Biorthogonal resource theory of genuine quantum superposition [0.0]
  We introduce a pseudo-Hermitian representation of the density operator, wherein its diagonal elements correspond to biorthogonal extensions of Kirkwood-Dirac quasi-probabilities. This representation provides a unified framework for the inter-basis quantum superposition and basis state indistinguishability, giving rise to what we term as textitgenuine quantum superposition.
  arXiv  Detail & Related papers  (2022-10-05T17:17:37Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving [0.0]
  We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We show that for the systems under consideration the generalised spectral form factor can be expressed in terms of dynamical correlation functions. This also provides a connection between the many-body Thouless time $tau_rm th$ -- the time at which the generalised spectral form factor starts following the random matrix theory prediction -- and the conservation laws of the system.
  arXiv  Detail & Related papers  (2020-10-23T15:54:55Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Theory of Ergodic Quantum Processes [0.0]
  We consider general ergodic sequences of quantum channels with arbitrary correlations and non-negligible decoherence. We compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned.
  arXiv  Detail & Related papers  (2020-04-29T18:00:03Z)

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.