Lanczos-Pascal approach to correlation functions in chaotic quantum systems

• URL: http://arxiv.org/abs/2503.17555v1
• Date: Fri, 21 Mar 2025 22:05:03 GMT
• Title: Lanczos-Pascal approach to correlation functions in chaotic quantum systems
• Authors: Merlin Füllgraf, Jiaozi Wang, Jochen Gemmer,
• Abstract summary: We find that the structure of the Lanczos coefficients that enables simpleness is in accord with the operator growth hypothesis.<n>We present a method to explicitly construct approximations to the dynamics from the Lanczos coefficients.<n>While the consideration applies to systems in the thermodynamic limit, we compare our approximations to state-of-the-art numerics for large but finite quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Equilibration is a ubiquitous phenomenon in chaotic quantum systems. Given the variety and multitude of condensed matter-type chaotic quantum systems, it may be considered as surprising how simple dynamics often are on the level of few body observables. In the context of this paper simple implies "in good agreement with a superpostion of only a few exponentially damped oscillations". We follow the (possibly somewhat odd) idea that it may be precisely the complexity of chaotic systems that entails the simpleness of their dynamics. We do so employing the framework of the recently resurged recursion method comprising Lanczos coefficients to generate the dynamics. We find that the structure of the Lanczos coefficients that enables simpleness is in accord with the operator growth hypothesis. We present a method to explicitly construct approximations to the dynamics from the Lanczos coefficients. These approximations result as simple for various chaotic spin systems. While the consideration applies to systems in the thermodynamic limit, we compare our approximations to state-of-the-art numerics for large but finite quantum systems and obtain good agreement.

Related papers

• Dynamics of Pseudoentanglement [0.03320194947871346]
  dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems.<n>Recent works have introduced a notion of pseudoentanglement describing ensembles of many-body states.<n>This prompts the question: how much entanglement is truly necessary to achieve thermal equilibrium in quantum systems?
  arXiv  Detail & Related papers  (2024-03-14T17:54:27Z)
• Predictive complexity of quantum subsystems [0.0]
  We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. Predictions are formed by equivalence classes of state vectors in the exterior Hilbert space. It can also serve as a local order parameter that can distinguish long and short range entanglement.
  arXiv  Detail & Related papers  (2023-09-26T18:58:56Z)
• 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)
• Quantum Lyapunov exponent in dissipative systems [68.8204255655161]
  The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. We study the interplay between these two processes. The OTOC decay rate is closely related to the classical Lyapunov.
  arXiv  Detail & Related papers  (2022-11-11T17:06:45Z)
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics [41.94295877935867]
  We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion. We apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model.
  arXiv  Detail & Related papers  (2022-09-07T15:50:00Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
  We propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
  arXiv  Detail & Related papers  (2021-04-13T17:24:08Z)
• Dynamical replica analysis of quantum annealing [0.0]
  An interesting alternative approach to the dynamics of quantum spin systems was proposed about a decade ago. It involves creating a proxy dynamics via the Suzuki-Trotter mapping of the quantum ensemble to a classical one. In this chapter we give an introduction to this approach, focusing on the ideas and assumptions behind the derivations.
  arXiv  Detail & Related papers  (2020-10-23T12:17:38Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)
• The entanglement membrane in chaotic many-body systems [0.0]
  In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an entanglement membrane'' in spacetime. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries.
  arXiv  Detail & Related papers  (2019-12-27T19:01:13Z)

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.