Related papers: Krylov Delocalization/Localization across Ergodici…
We propose a new approach to probing ergodicity and its breakdown in quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's…
We investigate operator delocalization in disordered one-dimensional spin chains by introducing -- besides the already known operator mass -- a complementary measure of operator complexity: the operator length. Like the operator…
In this paper, we studied a set of generalised Krylov complexity for operator growth. We demonstrate their universal features at both initial times and long times using half-analytical technique as well as numerical results. In particular,…
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…
In this work, we investigate the Krylov complexity in quantum optical systems subject to time--dependent classical external fields. We focus on various interacting quantum optical models, including a collection of two--level atoms, photonic…
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…
Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev…
Above the QCD chiral crossover temperature, the low-lying eigenmodes of the Dirac operator are localised, while moving up in the spectrum states become extended. This localisation/delocalisation transition has been shown to be a genuine…
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,…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
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…
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…
Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in…
The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to…
Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state…
Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has…
Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…
Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian…
Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at…
We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|\partial_t S_K|\leq 2b_1 \Delta S_K$, where $b_1$ is the first Lanczos…