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Related papers: Krylov complexity for non-local spin chains

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In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…

High Energy Physics - Theory · Physics 2026-04-23 Arpan Bhattacharyya , S. Shajidul Haque , Jeff Murugan , Mpho Tladi , Hendrik J. R. Van Zyl

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…

Quantum Physics · Physics 2022-06-07 Budhaditya Bhattacharjee , Xiangyu Cao , Pratik Nandy , Tanay Pathak

Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both…

High Energy Physics - Theory · Physics 2023-09-06 Johanna Erdmenger , Shao-Kai Jian , Zhuo-Yu Xian

Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The…

High Energy Physics - Theory · Physics 2023-08-21 Budhaditya Bhattacharjee , Pratik Nandy , Tanay Pathak

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…

Quantum Physics · Physics 2024-09-23 Heiko Georg Menzler , Rishabh Jha

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.…

Quantum Physics · Physics 2022-12-20 Seungjoo Baek

We investigate the phase transitions from chaotic to nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder, which can be realized with a Rydberg atom array setting. As the disorder strength increases, the emergence…

Quantum Physics · Physics 2025-10-03 Yijia Zhou , Wei Xia , Lin Li , Weibin Li

Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm…

Quantum Physics · Physics 2023-12-15 Aranya Bhattacharya , Pratik Nandy , Pingal Pratyush Nath , Himanshu Sahu

Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a…

Quantum Physics · Physics 2025-07-08 E. Medina-Guerra , I. V. Gornyi , Yuval Gefen

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time…

High Energy Physics - Theory · Physics 2021-10-04 Anatoly Dymarsky , Michael Smolkin

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…

High Energy Physics - Theory · Physics 2026-05-28 Ali Fatemiabhari , Carlos Nunez

Krylov complexity has emerged as a new probe of operator growth in a wide range of non-equilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space…

Quantum Physics · Physics 2023-03-14 Chenwei Lv , Ren Zhang , Qi Zhou

In this work, we investigate local quench dynamics in two-dimensional conformal field theories using Krylov space methods. We derive Lanczos coefficients, spread complexity, and Krylov entropies for local joining and splitting quenches in…

High Energy Physics - Theory · Physics 2025-10-21 Pawel Caputa , Giuseppe Di Giulio

Krylov complexity, a quantum complexity measure which uniquely characterizes the spread of a quantum state or an operator, has recently been studied in the context of quantum chaos. However, the definitiveness of this measure as a chaos…

Quantum Physics · Physics 2025-09-12 Sreeram PG , J. Bharathi Kannan , Ranjan Modak , S. Aravinda

The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…

Quantum Physics · Physics 2024-04-15 Liangyu Chen , Baoyuan Mu , Huajia Wang , Pengfei Zhang

We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…

High Energy Physics - Theory · Physics 2025-03-21 Peng-Zhang He , Hai-Qing Zhang

Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…

High Energy Physics - Theory · Physics 2024-01-01 Haifeng Tang

Out-of-time-order correlators (OTOC) in the Ising Floquet system, that can be both integrable and nonintegrable is studied. Instead of localized spin observables, we study contiguous symmetric blocks of spins or random operators localized…

Quantum Physics · Physics 2022-06-22 Rohit Kumar Shukla , Arul Lakshminarayan , Sunil Kumar Mishra

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in…

Quantum Physics · Physics 2023-12-22 Amin A. Nizami , Ankit W. Shrestha

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…

Quantum Physics · Physics 2025-02-05 Ben Craps , Oleg Evnin , Gabriele Pascuzzi