On Chord Dynamics and Complexity Growth in Double-Scaled SYK

• URL: http://arxiv.org/abs/2411.04251v2
• Date: Tue, 04 Feb 2025 00:49:06 GMT
• Title: On Chord Dynamics and Complexity Growth in Double-Scaled SYK
• Authors: Jiuci Xu,
• Abstract summary: We study the time evolution governed by the two-sided chord Hamiltonian in the double-scaled SYK model. We demonstrate how distinct semi-classical behaviors emerge by localizing within specific energy regions in the semi-classical limit.
• Score: 0.0
• License:
• Abstract: We study the time evolution governed by the two-sided chord Hamiltonian in the double-scaled SYK model, which induces a probability distribution over operators in the double-scaled algebra. Through the bulk-to-boundary map, this distribution translates into dynamical profiles of bulk states within the chord Hilbert space. We derive analytic expressions for such profiles, valid across a broad parameter range and all time scales. Additionally, we demonstrate how distinct semi-classical behaviors emerge by localizing within specific energy regions in the semi-classical limit. We revisit the doubled Hilbert space formalism as an isometric map between the one-particle sector of the chord Hilbert space and the doubled zero-particle sector. Utilizing this map, we obtain analytic results for correlation functions and investigate the dynamical properties of operator Krylov complexity for chords, establishing an equivalence between the chord number generating function and the crossed four-point correlation function. We also explore finite-temperature effects, showing that operator spreading slows as temperature decreases. In the semi-classical limit, we perform a saddle point analysis and incorporate the one-loop determinant to derive the normalized time-ordered four-point correlation function. The leading correction reproduces the \(1/N\) connected contribution observed in the large-\(p\) SYK model at infinite temperature. Finally, we examine the time evolution of operator Krylov complexity for a matter chord in the triple-scaled regime, linking it to the renormalized two-sided length in JT gravity with matter.

Related papers

• Krylov complexity of fermion chain in double-scaled SYK and power spectrum perspective [0.0]
  We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point functions, the analysis is performed in the limit where the two-point function becomes simple. We confirm the exponential growth of Krylov complexity in the very low temperature regime.
  arXiv  Detail & Related papers  (2024-07-18T08:47:05Z)
• 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)
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective [0.0]
  We analytically establish the linear growth of two sets of coefficients for any generic jump operators. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically.
  arXiv  Detail & Related papers  (2023-11-01T18:00:06Z)
• Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
  We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model. The two-mode Dicke model exhibits normal to superradiant quantum phase transition. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
  arXiv  Detail & Related papers  (2022-07-08T11:16:29Z)
• 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)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations [0.0]
  The quantum-critical properties of the transverse-field Ising model are investigated by means of quantum Monte Carlo. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range universality classes.
  arXiv  Detail & Related papers  (2021-03-17T07:00:29Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.