{"total":24,"items":[{"citing_arxiv_id":"2607.05294","ref_index":1,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity","primary_cat":"hep-th","submitted_at":"2026-07-06T16:37:39+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Changing the initial state to Q(H)|K0⟩ is exactly a Christoffel reweighting of the spectral measure by |Q|²; Krylov complexity then transfers from the reference problem through finite-band connectors and finite-rank kernel projections, with closed forms in Charlier, Krawtchouk and Chebyshev chains.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.01351","ref_index":5,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Wigner negativity in Krylov space and emergent semiclassicality","primary_cat":"hep-th","submitted_at":"2026-07-01T18:09:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.00074","ref_index":1,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Holographic Spread Complexity from Branes and Strings","primary_cat":"hep-th","submitted_at":"2026-06-30T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.23785","ref_index":16,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Controlled Chaos in 4D SCFTs","primary_cat":"hep-th","submitted_at":"2026-06-22T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.21662","ref_index":30,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"On the Universality of Probe Complexity in $\\mathcal{N}=4$ SYM","primary_cat":"hep-th","submitted_at":"2026-06-19T18:08:51+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.20790","ref_index":60,"ref_count":2,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Complexity Inequalities for Quantum Subsystems","primary_cat":"hep-th","submitted_at":"2026-06-18T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.03049","ref_index":126,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Holographic complexity of de-Sitter black holes","primary_cat":"hep-th","submitted_at":"2026-06-02T02:32:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Since the standard formula for computing this yields an imaginary result, the authors introduced a length scaleLr (an imaginary number) to make the complexity real. The codimension-one CV complexity is defined as CV ≡ V GNLr ,(1.1) whereVrepresents the extremal volume of the codimension-one timelike hypersurfaces. In [125], it was established that in the high-energy limit, the Krylov spread complexity [126] of the DSSYK corresponds to the length of a specific geodesic connecting past and future infinity in two-dimensional dS sine-dilaton gravity [127-131]. Generalizing this observation to generic dS spacetimes allows for the formulation of a novel complexity proposal: defining complexity as the volume of the timelike extremal surface anchored at the asymptotic future"},{"citing_arxiv_id":"2605.28681","ref_index":8,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Krylov complexity has it all","primary_cat":"hep-th","submitted_at":"2026-05-27T16:13:52+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Krylov complexity's Taylor coefficients recursively determine all Lanczos coefficients, making it a complete descriptor of operator dynamics, with caveats for spread complexity.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.17550","ref_index":14,"ref_count":3,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Krylov Correlators in $\\mathfrak{sl}(2,\\mathbb R)$ Models: Exact Results and Holographic Complexity","primary_cat":"hep-th","submitted_at":"2026-05-17T17:21:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16507","ref_index":5,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Krylov complexity from a simple quantum mechanical model for a radiating black hole","primary_cat":"hep-th","submitted_at":"2026-05-15T18:03:06+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A simplified mini-BMN matrix model for a radiating black hole exhibits early-time chaotic growth of Krylov complexity followed by late-time saturation to a plateau consistent with equilibration.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13956","ref_index":60,"ref_count":4,"confidence":0.9,"is_internal_anchor":false,"paper_title":"q-Askey Deformations of Double-Scaled SYK","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:01+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":2,"top_context_role":"method","top_context_polarity":"use_method","context_text":"limit of the theory, where the combinationqn is fixed,nbeing the chord number. On the one hand, one can build an ordered basis, called the Krylov basis, which minimises the cost function of a given evolving state, known as Krylov complexity [59, 60] (see recent reviews by [61-63]).3 This has found multiple applications in the literature, and it has been argued to be a concrete measure of quantum chaos (see [60, 65-68] among others). Recent developments show that Krylov complexity of the Hartle-Hawking (HH) state in the DSSYK model and some of its deformations can be precisely matched to the geodesic length between the Dirichlet boundaries of an AdS black hole [69] (several extensions have appeared in [27, 33, 47, 70-81]). Similarly, [47] showed that in the case of Al-Salam Chihara polynomials, Krylov"},{"citing_arxiv_id":"2605.07668","ref_index":69,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Bridging Krylov Complexity and Universal Analog Quantum Simulator","primary_cat":"quant-ph","submitted_at":"2026-05-08T12:39:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"1, 046121 (2024), arXiv:2408.14697 [quant-ph]. [67] D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, A Universal Operator Growth Hypothesis, Phys. Rev. X9, 041017 (2019), arXiv:1812.08657 [cond- mat.stat-mech]. [68] A. Avdoshkin, A. Dymarsky, and M. Smolkin, Krylov complexity in quantum field theory, and beyond, JHEP 06, 066, arXiv:2212.14429 [hep-th]. [69] V. Balasubramanian, P. Caputa, J. M. Magan, and Q. Wu, Quantum chaos and the complexity of spread of states, Phys. Rev. D106, 046007 (2022), arXiv:2202.06957 [hep-th]. [70] C. Liu, H. Tang, and H. Zhai, Krylov complexity in open quantum systems, Phys. Rev. Res.5, 033085 (2023), arXiv:2207.13603 [cond-mat.str-el]. [71] J. L. F. Barb' on, E. Rabinovici, R."},{"citing_arxiv_id":"2604.27054","ref_index":30,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"A Timelike Quantum Focusing Conjecture","primary_cat":"hep-th","submitted_at":"2026-04-29T18:00:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"8(2008), no. 10 0861-0899, [quant-ph/0701004]. [28] R. Jefferson and R. C. Myers,Circuit complexity in quantum field theory,JHEP10 (2017) 107, [arXiv:1707.08570]. [29] S. Chapman, M. P. Heller, H. Marrochio, and F. Pastawski,Toward a Definition of Complexity for Quantum Field Theory States,Phys. Rev. Lett.120(2018), no. 12 121602, [arXiv:1707.08582]. [30] V. Balasubramanian, P. Caputa, J. M. Magan, and Q. Wu,Quantum chaos and the complexity of spread of states,Phys. Rev. D106(2022), no. 4 046007, [arXiv:2202.06957]. [31] A. Bhattacharyya, A. Shekar, and A. Sinha,Circuit complexity in interacting QFTs and RG flows,JHEP10(2018) 140, [arXiv:1808.03105]. [32] H. A. Camargo, M. P. Heller, R. Jefferson, and J."},{"citing_arxiv_id":"2604.07432","ref_index":6,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Holographic Krylov Complexity for Charged, Composite and Extended Probes","primary_cat":"hep-th","submitted_at":"2026-04-08T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Avdoshkin and A. Dymarsky,Euclidean operator growth and quantum chaos,Phys. Rev. Res.2(2020) 043234 [1911.09672]. [4] A. Dymarsky and M. Smolkin,Krylov complexity in conformal field theory,Phys. Rev. D 104(2021) L081702 [2104.09514]. [5] P. Caputa, J. M. Magan and D. Patramanis,Geometry of Krylov complexity,Phys. Rev. Res. 4(2022) 013041 [2109.03824]. [6] V. Balasubramanian, P. Caputa, J. M. Magan and Q. Wu,Quantum chaos and the complexity of spread of states,Phys. Rev. D106(2022) 046007 [2202.06957]. [7] S. Baiguera, V. Balasubramanian, P. Caputa, S. Chapman, J. Haferkamp, M. P. Heller et al., Quantum complexity in gravity, quantum field theory, and quantum information science, 2503.10753. [8] E. Rabinovici, A."},{"citing_arxiv_id":"2603.29443","ref_index":61,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons","primary_cat":"hep-th","submitted_at":"2026-03-31T08:48:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"an averaged spectral form factor [30], gavg(t) = Z(β, t)Z ∗(β, t) J Z(β) 2 J ,(2.4) which exhibits significantly reduced fluctuations compared to the unaveraged quantity. 3For fixedl, the spectrum turns out to be linear. - 5 - Krylov complexity.Beyond traditional probes, Krylov complexity (KC) has emerged as a modern diagnostic of quantum chaos [61, 62]. It effectively captures the transition from integrability to chaos in a manner consistent with standard spectral diagnostics [63, 64]. While originally developed to characterize operator growth in the Heisenberg picture [65], the framework has been extended to the Schr¨ odinger picture to quantify the spread of states within the Krylov subspace [61]."},{"citing_arxiv_id":"2603.19359","ref_index":26,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas","primary_cat":"hep-th","submitted_at":"2026-03-19T18:00:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.11627","ref_index":7,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography","primary_cat":"hep-th","submitted_at":"2026-02-12T06:23:37+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.06113","ref_index":87,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography","primary_cat":"hep-th","submitted_at":"2026-02-05T19:00:00+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"1Also referred to as 1D TT deformations in the lower-dimensional case in [32, 33]. - 1 - AdS/CFT, which might carry some relevant lessons in higher dimensional holography. Key insights to understand the DSSYK model and its bulk dual include the double-scaled [58- 60] and chord [61] von Neumann algebras; the quantum group structure [62-67]; Krylov complexity [59, 68-85] for operators [86] and states [87] (see recent reviews in [88-90]);2 algebraic entanglement entropy [98, 99].3 However, there has been active debate about the specific bulk dual to the DSSYK model. The most-discussed bulk dual proposals include sine dilaton gravity [66, 92, 94, 109-114], and de Sitter (dS) space through different approaches, including Schwarzschild-dS3 space [81, 95, 96, 112, 115-117], and dS2 space as a s-wave"},{"citing_arxiv_id":"2601.09801","ref_index":8,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Probing the Chaos to Integrability Transition in Double-Scaled SYK","primary_cat":"hep-th","submitted_at":"2026-01-14T19:08:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"of quantum chaos behave across such transitions. There has been considerable interest in exploring various measures of quantum chaos including early-time measures such as out-of- time-ordered correlators (OTOCs)[1, 2], and late-time measures such as the spectral form factor [3]; level spacing spectral statistics [4-6]; Krylov complexity for operators [7] and states [8, 9]; see [10-12] for reviews. In particular, several works have found that Krylov complexity is a useful measure to characterize systems transitioning between chaotic and integrable properties [13-20]. In this work we consider the model of Berkooz, Brukner, Jia and Mamroud (BBJM) [21, 22] as a concrete framework to study a phase transition between integrable and chaotic"},{"citing_arxiv_id":"2511.03779","ref_index":108,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity","primary_cat":"hep-th","submitted_at":"2025-11-05T19:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"support","context_text":"2There are other proposals to holography of the DSSYK, which might be related one another [61, 65, 81]; most notably three-dimensional de Sitter (dS3) space from an observer-centric [61, 82-86] and stretched horizon [22, 87-95] perspectives; see also [96-101]. - 2 - been argued that one can deduce a precise notion of dS2 holographic complexity [102-107] as Krylov complexity [108, 109] (see [110-112] for reviews) in the DSSYK model. However, in a sharp contrast, entanglement entropy in the DSSYK model [113] and its place in the holographic dictionary beyond the AdS2 limit [114] remains much less developed than holographic complexity as Krylov complexity [64, 66, 81, 115-121]). So far, the literature has not addressed how to evaluate the entanglement entropy in the double-scaled algebras of"},{"citing_arxiv_id":"2510.22658","ref_index":2,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Toward Krylov-based holography in double-scaled SYK","primary_cat":"hep-th","submitted_at":"2025-10-26T12:40:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.14810","ref_index":51,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Krylov Complexity for Open Quantum System: Dissipation and Decoherence","primary_cat":"hep-th","submitted_at":"2025-09-18T10:12:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.04075","ref_index":13,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Complexity of Quadratic Quantum Chaos","primary_cat":"hep-th","submitted_at":"2025-09-04T10:09:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2507.23667","ref_index":50,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Universal Time Evolution of Holographic and Quantum Complexity","primary_cat":"hep-th","submitted_at":"2025-07-31T15:47:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}