相关论文: State Dependence of Krylov Complexity in $2d$ CFTs

We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm…

We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifications. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both…

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…

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…

We consider heavy-heavy-light-light (HHLL) correlators in AdS/CFT, focussing on the D1D5 CFT$_2$ and the ${\cal N}= 4$ super Yang-Mills theory. Out of the lightest $1/2$-BPS operator in the spectrum, $O$, we construct a particular heavy…

The subject matter of this work is a 1D quantum spin - $\frac{1}{2}$ chain associated with the inhomogeneous six-vertex model possessing an additional ${\cal Z}_r$ symmetry. The model is studied in a certain parametric domain, where it is…

We formulate a state-dependent definition of operator size that captures the effective size of an operator acting on a reference state. We apply our definition to the SYK model and holographic 2-dimensional CFTs, generalizing the…

We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…

In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…

In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…

The Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous…

In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature…

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar…

Since euclidean global AdS_2 space represented as a strip has two boundaries, the state / operator correspondence in the dual CFT_1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the…

We argue that the conventional method to calculate the OPE coefficients in the strong coupling limit for heavy-heavy-light operators in the N=4 Super-Yang-Mills theory has to be modified by integrating the light vertex operator not only…

We extend the CV conjecture to quantum states of two-mode Hermitian systems using the framework of information geometry. Specifically, we conjecture that the Krylov complexity of a quantum state equals the volume of the Fubini-Study metric.…

We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…

We investigated numerically the relationship between the lasing threshold, the density of states (DOS), and field localization in 1D photonic crystals (PC) for off-axis laser action. The angular dependence of the corresponding quantities…

In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an…

We calculate, for the first time, three-point correlation functions involving "heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong coupling. In particular, we focus on the three-point functions of the dilaton modes…