Critical spin models from holographic disorder

Dimitris Saraidaris; Alexander Jahn

doi:10.22331/q-2025-07-22-1808

Critical spin models from holographic disorder

Dimitris Saraidaris and Alexander Jahn

Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany

Published:	2025-07-22, volume 9, page 1808
Editor:	Carlo Beenakker
Eprint:	arXiv:2409.17235v2
Doi:	https://doi.org/10.22331/q-2025-07-22-1808
Citation:	Quantum 9, 1808 (2025).

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Abstract

Discrete models of holographic dualities, typically modeled by tensor networks on hyperbolic tilings, produce quantum states with a characteristic quasiperiodic disorder not present in continuum holography. In this work, we study the behavior of XXZ spin chains with such symmetries, showing that lessons learned from previous non-interacting (matchgate) tensor networks generalize to more generic Hamiltonians under holographic disorder: While the disorder breaks translation invariance, site-averaged correlations and entanglement of the disorder-free critical phase are preserved at a plateau of nonzero disorder even at large system sizes. In particular, we show numerically that the entanglement entropy curves in this disordered phase follow the expected scaling of a conformal field theory (CFT) in the continuum limit. This property is shown to be non-generic for other types of quasiperiodic disorder, only appearing when our boundary disorder ansatz is described by a "dual" bulk hyperbolic tiling. Our results therefore suggest the existence of a whole class of critical phases whose symmetries are derived from models of discrete holography.

Featured image: Building a critical Hamiltonian from a Multi-scale Quasicrystal Ansatz (MQA).

Popular summary

Holographic bulk/boundary dualities relate physics on a higher-dimensional bulk geometry to a lower-dimensional boundary. In a widely studied continuum bulk/boundary duality known as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, a bulk theory of (quantum) gravity with hyperbolic geometry is related to a boundary quantum theory on flat spacetime without gravity. One can capture aspects of this correspondence with tensor networks, which replace the bulk geometry by a discretized lattice, and produce finite-dimensional boundary states that resemble CFTs in a continuum limit. However, this discretization introduces new symmetries not present in the continuum case: Under a regular hyperbolic discretization of the bulk, the boundary theory exhibits quasiperiodic symmetries, i.e., a form of approximate self-similarity of local observables.

In our work, we study spin models with the quasiperiodic symmetries expected of such discrete boundary systems, described by an analytical multi-scale quasicrystal ansatz (MQA). We show that those spin systems that are in a critical phase (i.e., one with a CFT continuum limit) without any disorder retain their critical properties when MQA disorder is gradually increased, only becoming non-critical – diagnosed by entanglement saturation for larger subsystems and exponential decay of correlations – when the disorder strength becomes very large. In particular, this behavior also appears in interacting spin chains, a regime not accessible to simpler Gaussian techniques that we instead probe using the numerical Density Matrix Renormalization Group (DMRG) algorithm. These interacting, disordered spin systems are of particular interest to holography, where boundary theories are typically studied in a strongly-interacting regime. We also sharpen the relationship to holography by considering versions of the MQA that are not described by a unique "bulk geometry": Such models show qualitative differences to the "holographic" MQA, with MQA disorder now changing the critical phase. We also consider other types of quasiperiodic disorder, which likewise destabilize criticality when applied to a disorder-free spin chain.

These results suggest the existence of a disordered critical phase characterized by discrete-holographic boundary symmetries, appearing generically in both interacting and non-interacting spin chains. As these symmetries match those of a discretized higher-dimensional hyperbolic bulk, it appears that they stabilize critical properties similarly to how AdS bulk symmetries enforce CFT boundary symmetries in continuum holography. Our work thus provides a further step towards understanding the boundary side of discrete holography, and shows how holographic dualities can shed new light on quantum many-body phases.

► BibTeX data

@article{Saraidaris2025criticalspinmodels,
  doi = {10.22331/q-2025-07-22-1808},
  url = {https://doi.org/10.22331/q-2025-07-22-1808},
  title = {Critical spin models from holographic disorder},
  author = {Saraidaris, Dimitris and Jahn, Alexander},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1808},
  month = jul,
  year = {2025}
}

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