Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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Quantum complexity in gravity, quantum field theory, and quantum information science,
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q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
Mini-boson stars in AdS spacetime are proposed as holographic realizations of quantum scars, exhibiting chaotic spectra with integrable subsectors, anomalously low entanglement, and robust Krylov complexity revivals.
Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
Krylov complexity remains nonsingular at SWSSB crossovers but shows a singular area-to-volume-law transition at genuine mixed-state SWSSB phase transitions in dephasing channels.
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.
In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in the SL(3,R) subalgebra.
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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.
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.
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to test dependence only on coarse thermodynamic data.
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
Krylov complexity is equivalent to Lanczos coefficients, return amplitude, and spectral density for operator dynamics, via an explicit recursive algorithm from its t=0 Taylor expansion.
In the BMN matrix model and its holographic duals, Krylov basis states and Lanczos coefficients are uniquely fixed by the model's mass parameter.
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.
Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensitive to decoherence onset because the Krylov basis differs from the conventional one
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.
Generalizes Nielsen complexity to multiple cost factors, derives modified Euler-Arnold and Jacobi equations, and examines effects on conjugate points in single-qubit and SYK systems.
citing papers explorer
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
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Quantum scars from holographic boson stars
Mini-boson stars in AdS spacetime are proposed as holographic realizations of quantum scars, exhibiting chaotic spectra with integrable subsectors, anomalously low entanglement, and robust Krylov complexity revivals.
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Holographic Krylov Complexity for Charged, Composite and Extended Probes
Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
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Krylov Complexity and Mixed-State Phase Transition
Krylov complexity remains nonsingular at SWSSB crossovers but shows a singular area-to-volume-law transition at genuine mixed-state SWSSB phase transitions in dephasing channels.
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Universal Time Evolution of Holographic and Quantum Complexity
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.
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Violation of Universal Operator Growth Hypothesis in $\mathcal{W}_3$Conformal Field Theories
In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in the SL(3,R) subalgebra.
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Wigner negativity in Krylov space and emergent semiclassicality
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
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Controlled Chaos in 4D SCFTs
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
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Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
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Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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Complexity and Operator Growth in Holographic 6d SCFTs
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.
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Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
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.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
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.
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Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
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On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
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On the Universality of Probe Complexity in $\mathcal{N}=4$ SYM
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to test dependence only on coarse thermodynamic data.
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Holographic complexity of de-Sitter black holes
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
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Krylov complexity has it all
Krylov complexity is equivalent to Lanczos coefficients, return amplitude, and spectral density for operator dynamics, via an explicit recursive algorithm from its t=0 Taylor expansion.
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Krylov complexity for Lin-Maldacena geometries and their holographic duals
In the BMN matrix model and its holographic duals, Krylov basis states and Lanczos coefficients are uniquely fixed by the model's mass parameter.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
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.
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Krylov Complexity for Open Quantum System: Dissipation and Decoherence
Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensitive to decoherence onset because the Krylov basis differs from the conventional one
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Complexity of Quadratic Quantum Chaos
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.
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Nielsen complexity with multiple cost factors
Generalizes Nielsen complexity to multiple cost factors, derives modified Euler-Arnold and Jacobi equations, and examines effects on conjugate points in single-qubit and SYK systems.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.