Related papers: Krylov Complexity in Lifshitz-type Scalar Field Th…
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…
Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this…
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 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…
In this work, we investigate local quench dynamics in two-dimensional conformal field theories using Krylov space methods. We derive Lanczos coefficients, spread complexity, and Krylov entropies for local joining and splitting quenches in…
In the study of quantum chaos diagnostics, considerable attention has been attributed to the Krylov complexity and spectrum form factor (SFF) for systems at infinite temperature. These investigations have unveiled universal properties of…
We consider the recursion method applied to a generic 2pt function of a quantum system and show, in full generality, that the temperature dependence of the corresponding Lanczos coefficients is governed by integrable dynamics. After an…
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…
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,…
This paper establishes that Krylov complexity contains the entire information about the dynamics of a quantum operator, extending the list of equivalent quantities that can serve this purpose, such as the Lanczos coefficients, the return…
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…
In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable…
This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM). Krylov complexity quantifies how an operator evolves over time by expanding it in a series of…
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 $\mathcal{K}(t)$…
Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the…
We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…
Krylov complexity is a novel observable for detecting quantum chaos, and an indicator of a possible gravity dual. In this paper, we compute the Krylov complexity and the associated Lanczos coefficients in the SU(2) Yang-Mills theory, which…
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…
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…
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…