Related papers: Krylov complexity in conformal field theory
We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional…
We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade…
Exponential growth in the out-of-time-order correlator (OTOC) is an important potential signature of quantum chaos. The OTOC is quite simple to calculate for squeezed states, whose applications are frequently found in quantum optics and…
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…
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 compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time.…
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has…
Understanding the complexity of quantum many-body systems has been attracting much attention recently for its fundamental importance in characterizing complex quantum phases beyond the scope of quantum entanglement. Here, we investigate…
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…
Discretizing the $\lambda \phi^4$ scalar field theory on a lattice yields a system of coupled anharmonic oscillators with quadratic and quartic potentials. We begin by analyzing the two coupled oscillators in the second quantization method…
In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and…
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…
Building on the pioneering work of \cite{Caputa:2024sux}, we propose a holographic description of spread complexity and its rate in 2D CFTs. By exploiting $SL(2,\mathbb{R})$ symmetry, we explicitly construct the Krylov basis, expressing…
We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation…
The disorder and a simple convex measure of complexity are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a power law distribution may…
We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric.…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum-classical…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
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…