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Quantum Physics, quant-ph, Condensed Matter, Strongly Correlated Electrons, cond-mat.str-el,High Energy Physics - Theory, hep-th
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.
