Path-dependent correlations in dynamically tuned Ising models and its short-time behavior: application of Magnus expansion

• URL: http://arxiv.org/abs/2311.01785v1
• Date: Fri, 3 Nov 2023 08:49:39 GMT
• Title: Path-dependent correlations in dynamically tuned Ising models and its short-time behavior: application of Magnus expansion
• Authors: Xin Wang, Bo Yang, Bo Zhang, and Bo Xiong
• Abstract summary: We study the buildup of antiferromagnetic (AF) correlation in the dynamically tuned Ising models. We apply Magnus expansion (ME) to derive the high-order analytic expression of the connected correlation functions. We find that the magnitude of AF correlation for the same Manhattan distance is proportional to the number of the shortest paths.
• Score: 22.883073860070954
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the buildup of antiferromagnetic (AF) correlation in the dynamically tuned Ising models which are realized by the Rydberg atomic system. In short-time scale, we apply Magnus expansion (ME) to derive the high-order analytic expression of the connected correlation functions and compare it with exactly numerical results for the different lattice geometries, e.g., 1D chain, $2 \times n$ lattice, and $n \times n$ lattice. It is shown that the high-order expansion is required to describe accurately the buildup of AF correlation in the quench dynamics. Moreover, through a 2D square lattice, we find that the magnitude of AF correlation for the same Manhattan distance is proportional to the number of the shortest paths in a sufficiently long time until long and distinct paths are involved significantly with the buildup of the correlation. Finally, we propose an applicable experimental setup to realize our findings.

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)
• Topological phases of extended Su-Schrieffer-Heeger-Hubbard model [0.4741080054419136]
  We show that an extended Su-Schrieffer-Heeger-Hubbard model exhibits rich topological phases, characterized by robust edge states against interaction. We quantify the properties of these edge states by analyzing spin correlation and second-order R'enyi entanglement entropy. Our work provides a paradigm studying topological properties in large interacting systems via the CP-AFQMC algorithm.
  arXiv  Detail & Related papers  (2024-05-16T13:44:03Z)
• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models [5.623221917573403]
  We first derive the effective theory for scramblons in a single cBSYK model. We then study the entanglement dynamics in cBSYK chains.
  arXiv  Detail & Related papers  (2023-01-09T07:37:09Z)
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models [0.0]
  We investigate the dynamical spreading of correlations after a quantum quench starting from a magnetically disordered state in the transverse-field Ising model at one (1D) and two spatial dimensions (2D) We analyze specifically the longitudinal and transverse spin-spin correlation functions at equal time with use of several methods. Our findings provide useful benchmarks for quantum simulation experiments of correlation spreading and theoretical refinement of the Lieb-Robinson bound in the future.
  arXiv  Detail & Related papers  (2023-01-04T02:02:21Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and $\mathrm{RP}^2$ models: zero-temperature phase transition versus finite-temperature crossover [0.0]
  We compare the two-dimensional classical Heisenberg and $mathrmRP2$ models. For the Heisenberg model, we find no signs of a finite-temperature phase transition. For the $mathrmRP2$ model, we observe an abrupt onset of scaling behaviour.
  arXiv  Detail & Related papers  (2022-02-15T17:35:15Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Correlation-induced steady states and limit cycles in driven dissipative quantum systems [0.0]
  We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. We characterize the spatial structure of the correlations in the steady state, as well as their temporal dynamics.
  arXiv  Detail & Related papers  (2020-01-15T18:38:39Z)
• Fast approximations in the homogeneous Ising model for use in scene analysis [61.0951285821105]
  We provide accurate approximations that make it possible to numerically calculate quantities needed in inference. We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field. The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
  arXiv  Detail & Related papers  (2017-12-06T14:24:34Z)

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.