Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains

• URL: http://arxiv.org/abs/2405.07545v2
• Date: Wed, 29 Jan 2025 13:13:45 GMT
• Title: Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Authors: Tabea Herrmann, Roland Brandau, Arnd Bäcker,
• Abstract summary: It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average eigenstate entanglement indeed approaches the random matrix result. We attribute the origin of the deviations for the kicked spin-chain models to the tensor-product structure of the Hilbert spaces.
• Score: 0.0
• License:
• Abstract: It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average eigenstate entanglement indeed approaches the random matrix result. However, the distribution of the eigenstate entanglement differs significantly. While for autonomous systems such deviations are expected, they are surprising for the more scrambling kicked systems. Similar deviations occur in a tensor-product random matrix model with all-to-all interactions. Therefore, we attribute the origin of the deviations for the kicked spin-chain models to the tensor-product structure of the Hilbert spaces. As a consequence, this would mean that such many body systems cannot be described by the standard random matrix ensembles.

Related papers

• Anomalous transport in U(1)-symmetric quantum circuits [41.94295877935867]
  Investigation of discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes.
  arXiv  Detail & Related papers  (2024-11-21T17:56:26Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• 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)
• Characterizing quantum chaoticity of kicked spin chains [0.0]
  Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics agree with those of random matrix theory. We demonstrate that even if both level spacing distribution and eigenvector statistics agree well with random matrix predictions, the entanglement entropy deviates from the expected Page curve.
  arXiv  Detail & Related papers  (2023-06-15T10:51:11Z)
• Markov chains with doubly stochastic transition matrices and application to a sequence of non-selective quantum measurements [0.0]
  A time-dependent finite-state Markov chain that uses doubly transition matrices is considered. entropy that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are studied.
  arXiv  Detail & Related papers  (2022-03-16T14:58:38Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• When Random Tensors meet Random Matrices [50.568841545067144]
  This paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. We show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric textitblock-wise random matrix.
  arXiv  Detail & Related papers  (2021-12-23T04:05:01Z)
• A Random Matrix Perspective on Random Tensors [40.89521598604993]
  We study the spectra of random matrices arising from contractions of a given random tensor. Our technique yields a hitherto unknown characterization of the local maximum of the ML problem. Our approach is versatile and can be extended to other models, such as asymmetric, non-Gaussian and higher-order ones.
  arXiv  Detail & Related papers  (2021-08-02T10:42:22Z)
• On Random Matrices Arising in Deep Neural Networks: General I.I.D. Case [0.0]
  We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. We use another, more streamlined, version of the techniques of random matrix theory to generalize the results of [22] to the case where the entries of the synaptic weight matrices are just independent identically distributed random variables with zero mean and finite fourth moment.
  arXiv  Detail & Related papers  (2020-11-20T14:39:24Z)
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model [0.0]
  We show that at large enough times the probability distribution agrees exactly with the prediction of Random Matrix Theory. This behaviour is due to a recently identified additional anti-unitary symmetry of the self-dual kicked Ising model.
  arXiv  Detail & Related papers  (2020-09-07T16:02:29Z)
• On Random Matrices Arising in Deep Neural Networks. Gaussian Case [1.6244541005112747]
  The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The problem has been considered in recent work by using the techniques of free probability theory.
  arXiv  Detail & Related papers  (2020-01-17T08:30:57Z)

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.