Related papers: Violation of Universal Operator Growth Hypothesis …
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's…
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…
Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation…
The operator growth hypothesis (OGH) is a technical conjecture about the behaviour of operators -- specifically, the asymptotic growth of their Lanczos coefficients -- under repeated action by a Liouvillian. It is expected to hold for a…
We study operator growth in many-body systems with on-site spins larger than $1/2$, considering both non-integrable and integrable regimes. Specifically, we compute Lanczos coefficients in the one- and two-dimensional Ising models for spin…
We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos…
We develop a geometric approach to operator growth and Krylov complexity in many-body quantum systems governed by symmetries. We start by showing a direct link between a unitary evolution with the Liouvillian and the displacement operator…
We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with $c>1$. This formula is valid when one or more of the operators has large dimension or --…
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 $T{\bar{T}}$, $J{\bar{T}}$,…
In the context of chaotic quantum many-body systems, we show that operator growth, as diagnosed by out-of-time-order correlators of local operators, also leaves a sharp imprint in out-of-time-order correlators of global operators. In…
In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow…
We study Krylov (spread) complexity in strongly coupled six-dimensional ${\cal N}=(1,0)$ superconformal field theories with holographic duals in massive type IIA supergravity. Extending recent holographic proposals relating Krylov…
We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator…
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…
We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However,…
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…
We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral…
Recently, the out-of-time-ordered correlator(OTOC) and Krylov complexity have been studied actively as a measure of operator growth. OTOC is known to exhibit exponential growth in chaotic systems, which was confirmed in many previous works.…
The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincar\'e symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading…
We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of <phi…