Related papers: State Dependence of Krylov Complexity in $2d$ CFTs
Thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, $\lambda_L\leq 2\pi /\beta$. We harness this bound to constrain the space of…
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.…
We investigate the holographic complexity of CFTs compactified on a circle with a Wilson line, dual to magnetized solitons in AdS$_4$ and AdS$_5$. These theories have a confinement-deconfinement phase transition as a function of the Wilson…
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 prove the instability of $d$-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension $h=d/2+i r$, with non-vanishing $ r\in\mathbb{R}$. From…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator \Phi with large dimension \Delta_\Phi ~ O(c) at spatial infinities in the thermal state. We…
In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor…
We consider conformal blocks of two heavy operators and an arbitrary number of light operators in a (1+1)-d CFT with large central charge. Using the monodromy method, these higher-point conformal blocks are shown to factorize into products…
Complexity is a fundamental characteristic of states within a quantum system. Its use is however mostly limited to bosonic systems, inhibiting its present applicability to supersymmetric theories. This is also relevant to its application to…
We consider a perturbative expansion of the Lanczos coefficients and the Krylov complexity for two-dimensional conformal field theories under integrable deformations. Specifically, we explore the consequences of $T{\bar{T}}$, $J{\bar{T}}$,…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
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…
We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere. The spread complexity is obtained by using a purely geometric formulation in terms of…
Krylov complexity has recently gained attention where the growth of operator complexity in time is measured in terms of the off-diagonal operator Lanczos coefficients. The operator Lanczos algorithm reduces the problem of complexity growth…
In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, von Neumann entropy and capacity of entanglement for…
We study a simple class of correlators with two heavy and two light operators both in the D1D5 CFT and in the dual AdS$_3 \times S^3 \times T^4$ description. On the CFT side we focus on the free orbifold point and discuss how these…
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…
We investigate operator growth in quantum systems with two-dimensional Schr\"odinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schr\"odinger algebra which is…
We study the complexity of holographic superconductors (Einstein-Maxwell-complex scalar actions in $d+1$ dimension) by the `complexity = volume' (CV) conjecture. First, it seems that there is a universal property: the superconducting phase…