Related papers: Universal chaotic dynamics from Krylov space
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…
In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can…
We study the statistical properties of the spread complexity in the Krylov space of quantum systems driven across a quantum phase transition. Using the diabatic Magnus expansion, we map the evolution to an effective one-dimensional hopping…
We introduce Krylov spread complexity in the context of black hole scattering by studying highly excited string states (HESS). Krylov complexity characterizes chaos by quantifying the spread of a state or operator under a known Hamiltonian.…
We investigate the anatomy and complexity of quantum states in Krylov space, in the ergodic and many-body localised (MBL) phases of a disordered, interacting spin chain. The Krylov basis generated by the Hamiltonian from an initial state…
We investigate the phase transitions from chaotic to nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder, which can be realized with a Rydberg atom array setting. As the disorder strength increases, the emergence…
We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans…
Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a…
Krylov complexity has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the Lyapunov exponent. We compute the Krylov and the…
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…
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…
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and…
Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of…
We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…
Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…
In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful…
In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow…
In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…