A bstract In semi-classical systems, the exponential growth of out-of-time-order correlator (OTOC) is believed to be hallmark quantum chaos. However, on several occasions, it has been argued that, even in integrable OTOC can grow exponentially due presence unstable saddle points phase space. this work, we probe such an system exhibiting saddle-dominated scrambling through Krylov complexity and associated Lanczos coefficients. realm universal operator hypothesis, demonstrate that coefficients...

We study the operator growth in open quantum systems with dephasing dissipation terms, extending Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by Markovian dynamics. introduce a notion ''operator size concentration'' which allows diagrammatic and combinatorial proof asymptotic linear behavior two sets Lanczos coefficients ($a_n$ $b_n$) large $q$ limit. corroborate semi-analytics finite $N$...

A bstract We use Krylov complexity to study operator growth in the q -body dissipative Sachdev-Ye-Kitaev (SYK) model, where dissipation is modeled by linear and random p Lindblad operators. In large limit, we analytically establish of two sets coefficients for any generic jump numerically verify this implementing bi-Lanczos algorithm, which transforms Lindbladian into a pure tridiagonal form. find that saturates inversely with strength, while timescale grows logarithmically. This akin...

Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using explicit formalism of Lanczos algorithm, usually known as forward scattering approximation in this context, we compute Krylov state (spread) complexity typical generated by time evolution PXP Hamiltonian, hosting such states. We show for N\'eel revives an approximate sense, while generic ETH-obeying always increases. This can be attributed to SU(2) structure corresponding...

A bstract Considering the large q expansion of Sachdev-Ye-Kitaev (SYK) model in two-stage limit, we compute Lanczos coefficients, Krylov complexity, and higher cumulants subleading order, along with t/q effects. The complexity naturally describes “size” distribution while encode richer information. We further consider double-scaled limit SYK at infinite temperature, where ~ $$ \sqrt{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>N</mml:mi> </mml:msqrt>...

We study thermalization slowing down of a quantum many-body spin system upon approach to two distinct integrability limits. Motivated by previous studies classical systems, we identify timescales: one Lyapunov timescale is extracted quantifying operator growth in time on an appropriately defined basis, while another ergodization related the statistics fluctuations time-evolved around its mean value based eigenstate hypothesis. Using paradigmatic Ising chain, find that both timescales diverge...

Capacity of entanglement (CoE), an information-theoretic measure entanglement, defined as the variance modular Hamiltonian, is known to capture deviation from maximal entanglement. We derive exact expression for average eigenstate CoE in fermionic Gaussian states a finite series, valid arbitrary bi-partition total system. Further, we consider complex Sachdev-Ye-Kitaev (${\mathrm{SYK}}_{2}$) model thermodynamic limit and obtain closed-form CoE. In this limit, becomes independent system size....

The Adiabatic Gauge Potential (AGP) is the generator of adiabatic deformations between quantum eigenstates. There are many ways to construct AGP operator and evaluate norm. Recently, it was proposed that a Gram-Schmidt-type algorithm can be used explicitly expression AGP. We employ version this approach by using Lanczos in terms Krylov vectors norm coefficients. It has advantage minimizing redundancies evaluating nested commutators analytic for operator. some simple systems. derive an...

We present a version of holographic correspondence where bulk solutions with sources localized on the screen are key objects interest, and not defined by their boundary values screen. can use this to calculate semi-classical correlators in fairly general spacetimes, including flat space timelike screens. find that our approach reduces standard Dirichlet-like approach, when restricted AdS. But more settings, analytic continuation Dirichlet Green function does lead Feynman propagator bulk. Our...

A bstract We discuss various aspects of HKLL bulk reconstruction for the free scalar field in AdS d +1 . First, we consider spacelike kernel non-normalizable mode global coordinates. construct it as a sum. In even dimensions, this can be reproduced using chordal Green’s function approach that propose. This puts results on an equal footing with literature normalizable mode. Poincaré AdS, present explicit sum general and odd dimensions both kernels. For generic scaling dimension ∆, these...

We use Krylov complexity to study operator growth in the $q$-body dissipative SYK model, where dissipation is modeled by linear and random $p$-body Lindblad operators. In large $q$ limit, we analytically establish of two sets coefficients for any generic jump numerically verify this implementing bi-Lanczos algorithm, which transforms Lindbladian into a pure tridiagonal form. find that saturates inversely with strength, while timescale grows logarithmically. This akin behavior other...

We study thermalization slowing down of a quantum many-body system upon approach to two distinct integrability limits. Motivated by previous studies classical systems, we identify time scales: one Lyapunov scale is extracted quantifying operator growth in an appropriately defined basis, while another ergodization related statistics fluctuations the time-evolved around its mean value based on eigenstate hypothesis. Using paradigmatic Quantum Ising chain find that both timescales diverge...

Krylov space methods provide an efficient framework for analyzing the dynamical aspects of quantum systems, with tridiagonal matrices playing a key role. Despite their importance, behavior such from chaotic to integrable states, transitioning through intermediate phase, remains unexplored. We aim fill this gap by considering properties matrix elements and associated basis vectors appropriate random ensembles. utilize Rosenzweig-Porter model as our primary example, which hosts fractal regime...

We study the operator growth in open quantum systems with dephasing dissipation terms, extending Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by Markovian dynamics. introduce a notion ''operator size concentration'' which allows diagrammatic and combinatorial proof asymptotic linear behavior two sets Lanczos coefficients ($a_n$ $b_n$) large $q$ limit. corroborate semi-analytics finite $N$...

We consider the analytic continuation of ($p+q$)-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$ signature, study conformal boundary resulting ``Klein space.'' Unlike familiar $(\ensuremath{-}+++\ensuremath{\cdots})$ now null infinity $\mathcal{I}$ has only one connected component. The spatial timelike infinities (${i}^{0}$ ${i}^{\ensuremath{'}}$) are quotients generalizations AdS spaces nonstandard signature. Together, $\mathcal{I}$, ${i}^{0}$, ${i}^{\ensuremath{'}}$ combine...

In this paper, we consider the HKLL bulk reconstruction procedure for $p$-form fields and graviton in empty AdS$_{d + 1}$. We derive spacelike kernels normalizable non-normalizable modes of $p$-forms Poincar\'e patch The are first derived via a mode-sum approach arbitrary even dimensions. appropriate AdS-covariant identified corresponding obtained these fields. present arguments casting terms AdS chordal distance. Introducing an antipodal-like mapping, cast form. An alternative derivation is...

Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using explicit formalism of Lanczos algorithm, usually known as forward scattering approximation in this context, we compute Krylov state (spread) complexity typical generated by time evolution PXP Hamiltonian, hosting such states. We show for Neel revives an approximate sense, while generic ETH-obeying always increases. This can be attributed to SU(2) structure corresponding...

We discuss various aspects of HKLL bulk reconstruction for the free scalar field in AdS$_{d+1}$. First, we consider spacelike kernel non-normalizable mode global coordinates. construct it as a sum. In even dimensions, this can be reproduced using chordal Green's function approach that propose. This puts AdS results on an equal footing with literature normalizable mode. Poincaré AdS, present explicit sum general and odd dimensions both kernels. For generic scaling dimension $Δ$, these...

Considering the large-$q$ expansion of Sachdev-Ye-Kitaev (SYK) model in two-stage limit, we compute Lanczos coefficients, Krylov complexity, and higher cumulants subleading order, along with $t/q$ effects. The complexity naturally describes "size" distribution, while encode richer information. We further consider double-scaled limit SYK$_q$ at infinite temperature, where $q \sim \sqrt{N}$. In such a find that scrambling time shrinks to zero, coefficients diverge. growth appears be...

We consider the analytic continuation of $(p+q)$-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$-signature, study conformal boundary resulting "Klein space". Unlike familiar $(-+++..)$ signature, now null infinity ${\mathcal I}$ has only one connected component. The spatial timelike infinities ($i^0$ $i'$) are quotients generalizations AdS spaces non-standard signature. Together, I}, i^0$ $i'$ combine produce topological $S^{p+q-1}$ as an $S^{p-1} \times S^{q-1}$ fibration...