Many-body quantum chaos and emergence of Ginibre ensemble

• URL: http://arxiv.org/abs/2207.12390v1
• Date: Mon, 25 Jul 2022 17:56:39 GMT
• Title: Many-body quantum chaos and emergence of Ginibre ensemble
• Authors: Saumya Shivam, Andrea De Luca, David A. Huse, Amos Chan
• Abstract summary: We establish a connection between many-body quantum chaotic (MBQC) systems and the Ginibre random matrix ensemble (GinUE) We show that the dual spectra of TI MBQC systems necessarily have non-trivial and universal correlations due to the existence of a linear ramp in the spectral form factor (SFF) Lastly, we remark that locality and the many-body nature of MBQC systems are required for the emergence of the GinUE in large system sizes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish a connection between many-body quantum chaotic (MBQC) systems and the Ginibre random matrix ensemble (GinUE) - namely that non-Hermitian GinUE behaviors emerge in spatially-extended MBQC systems in the space direction, just as Hermitian random matrix behaviours emerge in MBQC systems in the time direction. We demonstrate the emergence of GinUE firstly in translational invariant (TI) MBQC systems, which can be associated with dual transfer matrices with complex-valued spectra, before generalizing to spatially-random systems. We argue and demonstrate that the dual spectra of TI MBQC systems necessarily have non-trivial and universal correlations due to the existence of a linear ramp in the spectral form factor (SFF). We show that, firstly, the spectral statistics of the dual spectra, probed by the dissipative spectral form factor and spacing distribution, falls under the universality class of the GinUE, and in particular displays level repulsion in the complex plane. Secondly, we obtain an exact analytical expression of SFF for the GinUE, and show that it universally describes the SFF of TI MBQC systems in the scaling limit where $t$ and $L$ are large, while the ratio between $L$ and $L_{\mathrm{Th}}$, the many body Thouless length is fixed. Thirdly, we propose variations of Ginibre models accounting for time periodicity, such that the SFF of Floquet MBQC (with or without TI) can be analytically described, thereby removing the necessity of TI for the emergence of GinUE. Lastly, we remark that locality and the many-body nature of MBQC systems are required for the emergence of the GinUE in large system sizes.

Related papers

• On a Matrix Ensemble for Arbitrary Complex Quantum Systems [0.0]
  We study a variation of the eigenvector ensemble initially proposed by Deutsch for the foundations of the Eigenstate Thermalization Hypothesis (ETH) We focus on the remnants of system-specific information that modify the late-time behavior of correlation functions. We show that for small energy windows correlation functions defined by the new ensemble reduce to the predictions of the ETH.
  arXiv  Detail & Related papers  (2024-07-29T23:17:45Z)
• Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Models [47.294535652946095]
  We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) This is the first global convergence result for Gaussian mixtures with more than $2$ components.
  arXiv  Detail & Related papers  (2024-06-29T16:44:29Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Spectral form factor in chaotic, localized, and integrable open quantum many-body systems [5.849733770560258]
  We numerically study the spectral statistics of open quantum many-body systems (OQMBS) as signatures of quantum chaos (or the lack thereof) We show that the DSFF of chaotic OQMBS displays the $textitquadratic$ ramp-plateau behaviour of the Ginibre ensemble from random matrix theory.
  arXiv  Detail & Related papers  (2024-05-02T18:04:04Z)
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors [22.983795509221974]
  We experimentally measure the spectral form factor (SFF) to probe the presence or absence of chaos in quantum many-body systems. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates.
  arXiv  Detail & Related papers  (2024-03-25T16:59:00Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• 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)
• Many-Body Quantum Chaos and Space-time Translational Invariance [0.0]
  We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings. We numerically demonstrate, with simulations of two distinct circuit models, that in such a scaling limit, most microscopic details become unimportant.
  arXiv  Detail & Related papers  (2021-09-09T18:00:00Z)
• Reachable sets for two-level open quantum systems driven by coherent and incoherent controls [77.34726150561087]
  We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
  arXiv  Detail & Related papers  (2021-09-09T16:14:23Z)
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos [4.653419967010185]
  We show that DSFF successfully diagnoses dissipative quantum chaos. We show correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy (and time) scale. For dissipative quantum integrable systems, we show that DSFF takes a constant value except for a region in complex time.
  arXiv  Detail & Related papers  (2021-03-08T19:00:01Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)

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.