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Spread complexity as classical dilaton solutions

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arxiv 2302.10489 v2 pith:UBPC6B2F submitted 2023-02-21 hep-th

Arghya Chattopadhyay , Arpita Mitra , Hendrik J.R. van Zyl This is my paper · ORCID
classification hep-th
keywords complexitydilatonspacealgebrasclassicalgeometrichilbertkrylov
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We demonstrate a relation between Nielsen's approach towards circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating K\"ahler structures on the full projective Hilbert space of low rank algebras. This geometric structure of the states in the Hilbert space ensures that every unitary transformation of the associated algebras leave the metric and the symplectic forms invariant. We further associate a classical matter free Jackiw-Teitelboim (JT) gravity model with these state manifolds and show that the dilaton can be interpreted as the quantum mechanical expectation values of the symmetry generators. On the other hand we identify the dilaton with the spread complexity over a Krylov basis thereby proposing a geometric perspective connecting two different notions of complexity.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complexity measures in holographic cascading theories with multiscale dynamics

    hep-th 2026-08 accept novelty 6.0 of 10

    In holographic B8 gauge theories, complexity growth flattens near a walking conformal regime, while Krylov oscillation periods track the infrared scale and persist in screened, non-confining phases.

  2. Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity

    hep-th 2024-12 conditional novelty 6.0 of 10

    In the brickwall model of a BTZ black hole, hand-tuned Gaussian randomness at a stretched horizon reproduces random-matrix-theory spectral statistics and Krylov complexity peaks for scalar and fermionic probes.

  3. Spread complexity for the planar limit of holography

    hep-th 2024-12 reject novelty 6.0 of 10

    Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.

  4. Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems

    quant-ph 2024-11 conditional novelty 5.0 of 10

    The moments of the spreading-operator measurement distribution are generalized spread complexities, which for GUE Hamiltonians peak more sharply at higher order and obey a norm bound.

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