Boundary theories of critical matchgate tensor networks

• URL: http://arxiv.org/abs/2110.02972v2
• Date: Fri, 22 Apr 2022 02:20:54 GMT
• Title: Boundary theories of critical matchgate tensor networks
• Authors: Alexander Jahn, Marek Gluza, Charlotte Verhoeven, Sukhbinder Singh, Jens Eisert
• Abstract summary: Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
• Score: 59.433172590351234
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states.

Related papers

• Critical spin models from holographic disorder [49.1574468325115]
  We study the behavior of XXZ spin chains with a quasiperiodic disorder not present in continuum holography. Our results suggest the existence of a class of critical phases whose symmetries are derived from models of discrete holography.
  arXiv  Detail & Related papers  (2024-09-25T18:00:02Z)
• Emergent Ashkin-Teller criticality in a constrained boson model [0.0]
  We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition. We provide an effective Landau-Ginzburg theory for such a transition, and discuss the connection of our model to the universality model describing Rydberg atom arrays.
  arXiv  Detail & Related papers  (2023-11-20T19:00:03Z)
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models [4.467896011825295]
  We investigate the ground-state properties and phase transitions of two self-dual fracton spin models. We show that both models experience a strong first-order phase transition with an anomalous $L-(D-1)$ scaling. Our work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes.
  arXiv  Detail & Related papers  (2023-11-18T13:12:14Z)
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT [0.0]
  The Bethe lattice Ising model is a classical model of statistical mechanics for the phase transition. We show the underlying mechanism and the exact scaling dimensions for the power-law decay of boundary spin correlations. In addition, we find that the phase transition in the interior induces a crossover behavior of boundary spin correlations, depending on the depth of the corresponding correlation path.
  arXiv  Detail & Related papers  (2023-10-19T09:14:03Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Conformal Properties of Hyperinvariant Tensor Networks [0.0]
  We analyze the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain. We show two new sets of tensor decompositions which exhibit different properties from the original construction. We find that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra of several minimial model CFTs.
  arXiv  Detail & Related papers  (2020-12-17T14:06:15Z)
• 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)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.