Related papers: Krylov complexity from integrability to chaos
Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and…
Krylov complexity, a quantum complexity measure which uniquely characterizes the spread of a quantum state or an operator, has recently been studied in the context of quantum chaos. However, the definitiveness of this measure as a chaos…
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 $\mathcal{K}(t)$…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
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…
Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one…
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…
Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a…
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…
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 propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…
In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…
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…
Krylov complexity has been proposed as a diagnostic of chaos in non-integrable lattice and quantum mechanical systems, and if the system is chaotic, Krylov complexity grows exponentially with time. However, when Krylov complexity is applied…
We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to…
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…
The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…
Krylov complexity has recently emerged as a useful probe of operator growth and quantum dynamics in many-body systems and holographic dualities. In this paper we study its behavior in the Veneziano--Wosiek model, a supersymmetric matrix…
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…