We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension $d_q$ is controlled by $d_q(d_q-1)$, leading to a dimension-weighted equipartition that approaches the simple large-sector scaling $d_q^2/\sum_{q'}d_{q'}^2$. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.
Krylov state complexity, or spread complexity, has emerged as a sharp and versatile diagnostic of quantum chaos, information spreading, and many-body dynamics. Built from the Lanczos algorithm and grounded in the optimal-basis theorem, Krylov complexity thereby provides a robust spectroscopic window into quantum dynami...
We study the one-sided time evolution of thermofield double (TFD) states in random matrix theory, where the Hamiltonian is taken to be a $D\times D$ random matrix drawn from a unitarily invariant emsemble of Hermitian matrices. We argue that the Krylov basis with the maximally entangled state taken as the initial vecto...
Krylov and Lanczos approximations are used in quantum dynamics, quantum subspace methods, and Hamiltonian learning. A practical question is how long an $m$-dimensional Krylov truncation can be trusted. We argue that this time is fixed by causal propagation on the associated Jacobi chain. The relevant distance is not th...
Shunji Matsuura, Yoji Kawamura, J. Salfi et al.· 0 citations
We develop a microscopic phase-space description of the quantum Calogero model in the presence of an external harmonic confining potential. Building on the quantum Lax-pair structure, we construct a Hermitian Wigner operator whose expectation value obeys the exact phase-space evolution equation d_t rho + lambda d_x rho...
We study unitary quantum dynamics in noisy Brownian models with global continuous symmetries, such as $U(1)$ and $SU(2)$, focusing on R\'enyi entanglement entropies and hydrodynamic and non-hydrodynamic correlators. By mapping the averaged late-time dynamics to the low-energy physics of effective replica Hamiltonians,...
We develop a comprehensive theoretical framework for Carrollian quantum mechanics by performing systematic ultra-relativistic contractions of the Klein--Gordon equation in the limit $c \to 0$. This limiting process uncovers three distinct sectors---time-like, space-like, and hybrid---each governed by a Carroll-invarian...
M. Ahmadi-Jahmani· 0 citations
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