Projected state ensemble of a generic model of many-body quantum chaos

• URL: http://arxiv.org/abs/2402.16939v2
• Date: Tue, 10 Sep 2024 21:12:53 GMT
• Title: Projected state ensemble of a generic model of many-body quantum chaos
• Authors: Amos Chan, Andrea De Luca,
• Abstract summary: The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the $k$-th moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension $q$, we find that all moments converge simultaneously with a time scaling linearly in the size of region $A$, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite $q$ on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times $t_k = O(\log k)$. Our results are supported with numerical simulations performed at $q=2$.

Related papers

• 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)
• 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)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons [2.9491988705158843]
  We characterize the geometry of quantum states associated with different values of $kappa$, i.e., different quantum statistics. We characterize this decay using quantum speed limits on the flow of $kappa$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
  arXiv  Detail & Related papers  (2022-10-19T17:59:59Z)
• Simulability of high-dimensional quantum measurements [0.0]
  We demand that the statistics obtained from $mathcalM$ and an arbitrary quantum state $rho$ are recovered exactly by first compressing $rho$ into a lower dimensional space. A full quantum compression is possible, if and only if the set $mathcalM$ is jointly measurable. We analytically construct optimal simulation models for all projective measurements subjected to white noise or losses.
  arXiv  Detail & Related papers  (2022-02-25T21:22:29Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Provably accurate simulation of gauge theories and bosonic systems [2.406160895492247]
  We develop methods for bounding the rate of growth of local quantum numbers. For the Hubbard-Holstein model, we compute a bound on $Lambda$ that achieves accuracy $epsilon$. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution.
  arXiv  Detail & Related papers  (2021-10-13T18:00:02Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism [0.0]
  This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe. We use the $Out-of-Time Ordered correlation (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times.
  arXiv  Detail & Related papers  (2020-09-08T16:10:52Z)

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.