q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
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Quantum Dynamics in Krylov Space: Methods and Applications
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Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
A spectral-resolvent Krylov framework defines a distribution for quantum Fisher information and identifies universal exponential or algebraic convergence regimes based on the Liouville spectrum.
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
Recursion method extension to quench dynamics is limited by state-dependent quench coefficients c_n lacking universal structure, restricting accurate timescales except for favorable initial states.
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
In holographic 6d N=(1,0) SCFTs, generalized proper momentum of infalling particles grows linearly at late times, with early dynamics modified by SU(2)_R charge and quiver spreading.
Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-energy spectrum.
A multi-part truncation for lattice QCD with fermions enables explicit Hamiltonians in 1+1D and 2+1D and string-breaking simulations by capping basis states, electric energy, fermions per site, and using large-Nc matrix element scaling.
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
Derivative of Krylov spread complexity diverges logarithmically at SSH topological transitions and is bounded by fidelity susceptibility in general two-band Hamiltonians, with a non-unitary duality between phases.
The generalized dipole model fits entropy and mean multiplicity data from proton-proton collisions significantly better than the standard 1D Mueller dipole model.
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
Spread complexity is recovered as the infinitesimal-time limit of a circuit complexity defined by minimal-cost synthesis with time-evolution and beam-splitting operations.
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
Krylov complexity equals Fubini-Study volume for closed and open two-mode squeezed states, providing analytic support for the generalized CV conjecture via information geometry.
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Recursion method for out-of-equilibrium many-body dynamics: strengths and limitations
Recursion method extension to quench dynamics is limited by state-dependent quench coefficients c_n lacking universal structure, restricting accurate timescales except for favorable initial states.