Operator growth in open quantum systems: lessons from the dissipative SYK

B Bhattacharjee, X Cao, P Nandy, T Pathak - Journal of High Energy …, 2023‏ - Springer
A bstract We study the operator growth in open quantum systems with dephasing dissipation
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …

Universal chaotic dynamics from Krylov space

J Erdmenger, SK Jian, ZY **an - Journal of High Energy Physics, 2023‏ - Springer
A bstract 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 …

Operator dynamics in Lindbladian SYK: a Krylov complexity perspective

B Bhattacharjee, P Nandy, T Pathak - Journal of High Energy Physics, 2024‏ - Springer
A bstract We use Krylov complexity to study operator growth in the q-body dissipative
Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p …

Krylov complexity in quantum field theory, and beyond

A Avdoshkin, A Dymarsky, M Smolkin - Journal of High Energy Physics, 2024‏ - Springer
A bstract We study Krylov complexity in various models of quantum field theory: free massive
bosons and fermions on flat space and on spheres, holographic models, and lattice models …

Spread complexity for measurement-induced non-unitary dynamics and Zeno effect

A Bhattacharya, RN Das, B Dey… - Journal of High Energy …, 2024‏ - Springer
A bstract Using spread complexity and spread entropy, we study non-unitary quantum
dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the …

Quantum dynamics in Krylov space: Methods and applications

P Nandy, AS Matsoukas-Roubeas… - arxiv preprint arxiv …, 2024‏ - arxiv.org
The dynamics of quantum systems unfolds within a subspace of the state space or operator
space, known as the Krylov space. This review presents the use of Krylov subspace …

Spread and spectral complexity in quantum spin chains: from integrability to chaos

HA Camargo, KB Huh, V Jahnke, HS Jeong… - Journal of High Energy …, 2024‏ - Springer
A bstract We explore spread and spectral complexity in quantum systems that exhibit a
transition from integrability to chaos, namely the mixed-field Ising model and the next-to …

Spread complexity as classical dilaton solutions

A Chattopadhyay, A Mitra, HJR Van Zyl - Physical Review D, 2023‏ - APS
We demonstrate a relation between Nielsen's approach toward circuit complexity and Krylov
complexity through a particular construction of quantum state space geometry. We start by …

Dynamical actions and q-representation theory for double-scaled SYK

A Blommaert, TG Mertens, S Yao - Journal of High Energy Physics, 2024‏ - Springer
A bstract We show that DSSYK amplitudes are reproduced by considering the quantum
mechanics of a constrained particle on the quantum group SU q (1, 1). We construct its left …

Krylov complexity in Lifshitz-type scalar field theories

MJ Vasli, KB Velni, MRM Mozaffar, A Mollabashi… - The European Physical …, 2024‏ - Springer
We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar
theories, characterized by their integer dynamical exponent, at finite temperature. In this non …