Highly entangled spin chains and 2D quantum gravity

• URL: http://arxiv.org/abs/2005.00257v3
• Date: Mon, 1 Jun 2020 11:15:40 GMT
• Title: Highly entangled spin chains and 2D quantum gravity
• Authors: Fumihiko Sugino
• Abstract summary: Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume. We introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3/2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity.

Related papers

• Exponential onset of scalable entanglement via twist-and-turn dynamics in XY models [41.94295877935867]
  We show that the so-called twist-and-turn" (TaT) dynamics can offer an important resource to reach scalable multipartite entanglement.<n>For dipolar interactions, the entanglement dynamics at intermediate times is completely at odds with thermalization.
  arXiv  Detail & Related papers  (2025-07-10T22:34:44Z)
• Quantum channel for modeling spin-motion dephasing in Rydberg chains [44.99833362998488]
  We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions.<n>We benchmark the accuracy of our approach against exact diagonalization for small systems, identifying its regime of validity and the onset of perturbative breakdown.<n>We then apply the quantum channel to compute fidelity loss during transport of single-spin excitations across extended Rydberg chains in intractable regimes via exact diagonalization.
  arXiv  Detail & Related papers  (2025-06-30T17:37:38Z)
• 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)
• Probing critical phenomena in open quantum systems using atom arrays [3.365378662696971]
  At quantum critical points, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions. Here, we employ a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice. By accounting for and tuning the openness of our quantum system, we are able to directly observe power-law correlations and extract the corresponding scaling dimensions.
  arXiv  Detail & Related papers  (2024-02-23T15:21:38Z)
• Scalable spin squeezing in two-dimensional arrays of dipolar large-$S$ spins [0.0]
  We show that spin-spin interactions lead to scalable spin squeezing along the non-equilibrium unitary evolution in a coherent spin state. For sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting (OAT) model. Spin squeezing with OAT-like scaling is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts.
  arXiv  Detail & Related papers  (2023-09-11T10:32:24Z)
• Quantum collapse and exponential growth of out-of-time-ordered correlator in anisotropic quantum Rabi model [10.967081346848687]
  We show that the exponential growth of the out-of-time-ordered correlator (OTOC) at early times for the initial states centered both in the chaotic and stable regions of the anisotropic quantum Rabi model. We attribute the exponential growth of the OTOC to quantum collapse which provides a novel mechanism of yielding exponential growth of the OTOC in quantum systems. Our results show that compared with the OTOC, the linear entanglement entropy and Loschmidt echo seem to be more effective to diagnose the signals of quantum chaos in the anisotropic quantum Rabi model.
  arXiv  Detail & Related papers  (2023-05-27T15:23:37Z)
• Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems [0.0]
  Central spin systems are paradigmatic models for nitrogen-vacancy centers and quantum dots. Here, we derive exact results on the emergent behavior of open quantum central spin systems. Our findings may become relevant for developing fully quantum descriptions of many-body solid-state devices.
  arXiv  Detail & Related papers  (2023-05-24T20:23:31Z)
• 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)
• Many-body quantum chaos in stroboscopically-driven cold atoms [0.0]
  In quantum chaotic systems, the spectral form factor (SFF) is known to follow random matrix theory (RMT) We show the existence of the 'bump-ramp-plateau' behavior in the SFF for a number of paradigmatic and stroboscopically-driven 1D cold atom models.
  arXiv  Detail & Related papers  (2022-10-07T22:27:08Z)
• Noisy induced entanglement transition in one-dimensional random quantum circuits [8.424620634789127]
  We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity.
  arXiv  Detail & Related papers  (2022-03-15T11:15:11Z)
• Entropy decay for Davies semigroups of a one dimensional quantum lattice [13.349045680843885]
  We show that the relative entropy between any evolved state and the equilibrium Gibbs state contracts exponentially fast with an exponent that scales logarithmically with the length of the chain. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2021-12-01T16:15:58Z)
• Rapid thermalization of spin chain commuting Hamiltonians [13.349045680843885]
  We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2021-12-01T16:08:10Z)
• Generating Function for Tensor Network Diagrammatic Summation [0.24499092754102875]
  We introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain.
  arXiv  Detail & Related papers  (2021-01-11T14:55:27Z)
• Exponential enhancement of quantum metrology using continuous variables [15.102680713021368]
  We propose a new design of the signal-probe Hamiltonian which generates an exponential enhancement of measurement sensitivity. We show that linear scaling in both time and the number of coupling terms is sufficient to obtain exponential enhancement.
  arXiv  Detail & Related papers  (2020-04-02T18:20:05Z)

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.