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Related papers: Krylov Complexity, Confinement and Universality

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Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and…

Quantum Physics · Physics 2025-02-05 Ben Craps , Oleg Evnin , Gabriele Pascuzzi

Dynamical quantum phase transitions, encompassing phenomena like many-body localization transitions and measurement-induced phase transitions, are often characterized and identified through the analysis of quantum entanglement. Here, we…

Quantum Physics · Physics 2024-10-15 Wei Xia , Jie Zou , Xiaopeng Li

We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…

Other Condensed Matter · Physics 2009-10-06 Thierry Platini , Dragi Karevski , Loïc Turban

We continue the analysis of the Krylov complexity in the IP matrix model. In a previous paper, for a fundamental operator, it was shown that at zero temperature, the Krylov complexity oscillates and does not grow, but in the infinite…

High Energy Physics - Theory · Physics 2023-08-17 Norihiro Iizuka , Mitsuhiro Nishida

We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, i.e. anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates…

Numerical Analysis · Mathematics 2026-02-26 Pietro Benedusi , Simone Riva , Luca Belluzzi , Stefano Serra-Capizzano

The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…

Quantum Physics · Physics 2023-09-26 Gastón F. Scialchi , Augusto J. Roncaglia , Diego A. Wisniacki

We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent $z$. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov…

High Energy Physics - Theory · Physics 2025-11-11 Hamid R. Imani , Komeil Babaei Velni , M. Reza Mohammadi Mozaffar

In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…

High Energy Physics - Theory · Physics 2026-02-12 Matteo Baggioli , Kyoung-Bum Huh , Hyun-Sik Jeong , Xuhao Jiang , Keun-Young Kim , Juan F. Pedraza

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in…

Quantum Physics · Physics 2023-12-22 Amin A. Nizami , Ankit W. Shrestha

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the…

High Energy Physics - Theory · Physics 2026-05-26 Dibakar Roychowdhury

We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the…

Quantum Physics · Physics 2026-04-16 Rahul Gupta , Florian Mintert , Himadri Shekhar Dhar

Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of…

High Energy Physics - Theory · Physics 2022-09-13 Wolfgang Mück , Yi Yang

The IP matrix model is a simple large $N$ quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. It is a model introduced previously as a toy model of the gauge theory dual of an AdS black…

High Energy Physics - Theory · Physics 2023-06-09 Norihiro Iizuka , Mitsuhiro Nishida

In this paper we study Krylov complexity in the presence of single and multiple operators in the DSSYK model, where we can use the analytical techniques coming from chord diagrammatics. One of the results we obtain is that it showcases the…

High Energy Physics - Theory · Physics 2025-11-12 Marco Ambrosini , Eliezer Rabinovici , Julian Sonner

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative…

High Energy Physics - Theory · Physics 2024-04-02 Hugo A. Camargo , Viktor Jahnke , Keun-Young Kim , Mitsuhiro Nishida

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…

Quantum Physics · Physics 2026-04-21 Kazutaka Takahashi , Pratik Nandy , Adolfo del Campo

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open…

General Relativity and Quantum Cosmology · Physics 2026-02-27 Shi-Cheng Liu , Lei-Hua Liu , Bichu Li , Hai-Qing Zhang , Peng-Zhang He

The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a pre-defined basis. It is known that this complexity is minimised by choosing the Krylov basis, thus defining…

Quantum Physics · Physics 2024-09-04 Amin A. Nizami , Ankit W. Shrestha

Heisenberg time evolution under a chaotic many-body Hamiltonian $H$ transforms an initially simple operator into an increasingly complex one, as it spreads over Hilbert space. Krylov complexity, or `K-complexity', quantifies this growth…

High Energy Physics - Theory · Physics 2021-06-30 E. Rabinovici , A. Sánchez-Garrido , R. Shir , J. Sonner

The symmetry-resolved Krylov complexity is a useful tool in studying chaotic properties of systems that are endowed with symmetries. We investigate the conditions under which an invariant operator would have the symmetry-resolved Krylov…

High Energy Physics - Theory · Physics 2026-04-08 Shaliya Kotta , P N Bala Subramanian