Superspin Renormalization and Slow Relaxation in Random Spin Systems

• URL: http://arxiv.org/abs/2502.09612v1
• Date: Thu, 13 Feb 2025 18:59:03 GMT
• Title: Superspin Renormalization and Slow Relaxation in Random Spin Systems
• Authors: Yi J. Zhao, Samuel J. Garratt, Joel E. Moore,
• Abstract summary: We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-$frac12$ systems. Our formalism is suitable for systems with $textrmU(1)$ and $mathbbZ$ symmetries, and we apply it to chains of randomly positioned spins with dipolar $XX+YY$ interactions.
• Score: 0.0
• License:
• Abstract: We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-$\frac{1}{2}$ systems. Our formalism is suitable for systems with $\textrm{U}(1)$ and $\mathbb{Z}_2$ symmetries, and we apply it to chains of randomly positioned spins with dipolar $XX+YY$ interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians which provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve ``superspins'': two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor $XX+YY$ chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the local spin survival probability $\overline{S_p}(t)$, we demonstrate quantitative agreement in results between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of $\overline{S_p}(t)$ slower than any power law and feature no significant deviation from the $\sim 1/ \log^2(t)$ asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of $\overline{S_p}(t)$.

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)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Entanglement Entropy Growth in Disordered Spin Chains with Tunable Range Interactions [0.0]
  We study the effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics. For $alphaalpha_c$, we find that the entanglement entropy grows as a power-law with time.
  arXiv  Detail & Related papers  (2023-03-04T13:27:56Z)
• Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian [0.0]
  approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) We consider the system with the intensity of the spin-spin interaction $sim 1/ralpha$, $alphage 3$, and find the low boundary $alpha_c$ of applicability of the NNI to the evolution of an arbitrary one-excitation initial quantum state in the homogeneous spin chain governed by the $XX$-Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-23T15:01:12Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• A Law of Robustness beyond Isoperimetry [84.33752026418045]
  We prove a Lipschitzness lower bound $Omega(sqrtn/p)$ of robustness of interpolating neural network parameters on arbitrary distributions. We then show the potential benefit of overparametrization for smooth data when $n=mathrmpoly(d)$. We disprove the potential existence of an $O(1)$-Lipschitz robust interpolating function when $n=exp(omega(d))$.
  arXiv  Detail & Related papers  (2022-02-23T16:10:23Z)
• Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors [0.0]
  cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain. We analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions.
  arXiv  Detail & Related papers  (2021-03-07T05:20:52Z)
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model [0.0]
  It is possible to simulate the dynamics of a single spin-$1/2$ ($mathsfPT$ symmetric) system by embedding it into a subspace of a larger Hilbert space with unitary dynamics. We visualize it as a strongly correlated central spin model with the additional spin-$1/2$ playing the role of central spin.
  arXiv  Detail & Related papers  (2020-12-24T19:00:11Z)
• Debiased Sinkhorn barycenters [110.79706180350507]
  Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. We show how this bias is tightly linked to the reference measure that defines the entropy regularizer. We propose debiased Wasserstein barycenters that preserve the best of both worlds: fast Sinkhorn-like iterations without entropy smoothing.
  arXiv  Detail & Related papers  (2020-06-03T23:06:02Z)
• Spin squeezing with short-range spin-exchange interactions [0.0]
  We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance $r$ as $1/ralpha$ in $D=2$ and $3$ spatial dimensions. A region of "collective" behavior in which optimal squeezing grows with system size extends all the way to the $alphatoinfty$ limit of nearest-neighbor interactions.
  arXiv  Detail & Related papers  (2020-06-01T05:11:12Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.