English
Related papers

Related papers: Universal chaotic dynamics from Krylov space

200 papers

We study quenched dynamics of fully-connected spin models. The system is prepared in a ground state of the initial Hamiltonian and the Hamiltonian is suddenly changed to a different form. We apply the Krylov subspace method to map the…

Quantum Physics · Physics 2025-08-20 Kazutaka Takahashi

Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by…

Quantum Physics · Physics 2024-04-19 Ben Craps , Oleg Evnin , Gabriele Pascuzzi

We analyze the properties of Krylov state complexity in qubit dynamics, considering a single qubit and a qubit pair. A geometrical picture of the Krylov complexity is discussed for the single-qubit case, whereas it becomes non-trivial for…

Quantum Physics · Physics 2025-04-18 Siddharth Seetharaman , Chetanya Singh , Rejish Nath

We investigate the appearance of quantum chaos in a single many-body wave function by analyzing the statistical properties of the eigenvalues of its reduced density matrix $\rho_A$ of a spatial subsystem A. We find that the spectrum of…

Strongly Correlated Electrons · Physics 2018-09-12 Xiao Chen , Andreas W. W. Ludwig

In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed…

Statistical Mechanics · Physics 2026-02-20 Xuhao Jiang , Jad C. Halimeh , N. S. Srivatsa

Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a…

Quantum Physics · Physics 2025-03-11 Aranya Bhattacharya , Pingal Pratyush Nath , Himanshu Sahu

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as…

High Energy Physics - Theory · Physics 2023-02-08 Pawel Caputa , Nitin Gupta , S. Shajidul Haque , Sinong Liu , Jeff Murugan , Hendrik J. R. Van Zyl

Krylov complexity has emerged as a new probe of operator growth in a wide range of non-equilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space…

Quantum Physics · Physics 2023-03-14 Chenwei Lv , Ren Zhang , Qi Zhou

We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and…

Quantum Physics · Physics 2026-01-28 Carlo Cafaro , Emma Clements , Vishnu Vardhan Anuboyina

Strongly interacting quantum many-body systems are expected to thermalize, however, some evade thermalization due to symmetries. Quantum synchronization provides one such example of ergodicity breaking, but previous studies have focused on…

Disordered Systems and Neural Networks · Physics 2026-02-13 Nicolas Loizeau , Berislav Buča

Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm…

Quantum Physics · Physics 2023-12-15 Aranya Bhattacharya , Pratik Nandy , Pingal Pratyush Nath , Himanshu Sahu

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric…

High Energy Physics - Theory · Physics 2023-04-27 Bao-ning Du , Min-xin Huang

In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…

Quantum Physics · Physics 2024-11-05 Saud Čindrak , Adrian Paschke , Lina Jaurigue , Kathy Lüdge

Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…

Quantum Physics · Physics 2026-03-10 Saud Čindrak , Kathy Lüdge

We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site…

Quantum Physics · Physics 2025-12-22 J. T. Chalker , Dominik Hahn

We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We…

High Energy Physics - Theory · Physics 2024-09-04 Hugo A. Camargo , Kyoung-Bum Huh , Viktor Jahnke , Hyun-Sik Jeong , Keun-Young Kim , Mitsuhiro Nishida

We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…

Quantum Physics · Physics 2025-04-29 Ankit Gill , Tapobrata Sarkar

The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…

Chaotic Dynamics · Physics 2009-11-07 S. M. Soskin , O. M. Yevtushenko , R. Mannella

We characterize the Many-Body Localization (MBL) phase transition using the dynamics of spread complexity and inverse participation ratio in the Krylov space starting from different initial states. Our analysis of the disordered Heisenberg…

Disordered Systems and Neural Networks · Physics 2024-09-05 Maitri Ganguli , Aneek Jana

We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average…

Quantum Physics · Physics 2025-03-20 Zhuoran Li , Wei Fan