Related papers: Krylov complexity in the IP matrix model II
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…
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 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…
This paper develops a new class of exponential-type integrators where all the matrix exponentiations are performed in a single Krylov space of low dimension. The new family, called Lightly Implicit Krylov-Exponential (LIKE), is well suited…
We consider the approximation of $B^T (A+sI)^{-1} B$ where $A\in\mathbb{R}^{n\times n}$ is large, symmetric positive definite, and has a dense spectrum, and $B\in\mathbb{R}^{n\times p}$, $p\ll n$. Our target application is the computation…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
Solving short and long time dynamics of closed quantum many-body systems is one of the main challenges of both atomic and condensed matter physics. For locally interacting closed systems, the dynamics of local observables can always be…
We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for…
Krylov subspace methods quantify operator growth in quantum many-body systems through Lanczos coefficients that encode how operators spread under time evolution. Although these diagnostics were originally motivated by questions of chaos and…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is confined to an ellipse not including the origin, convergence is exponential, with the same…
We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in…
The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…
This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA)…
We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic…
In this paper we study the notion of complexity under time evolution in chaotic quantum systems with holographic duals. Continuing on from our previous work, we turn our attention to the issue of Krylov complexity upon the insertion of a…
We show how to expand the free energy of a matrix model coupled to arbitrary matter in powers of the matter coupling constant. Concentrating on $\nu$ uncoupled Ising models---which have central charge $\nu/2$---we work out the expansion to…
The abstract issue of 'Krylov solvability' is extensively discussed for the inverse problem $Af = g$ where $A$ is a (possibly unbounded) linear operator on an infinite-dimensional Hilbert space, and $g$ is a datum in the range of $A$. The…
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…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…