Stability of exponentially damped oscillations under perturbations of the Mori-Chain

Heveling, Robin; Wang, Jiaozi; Bartsch, Christian; Gemmer, Jochen

doi:10.1088/2399-6528/ac863b

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…This is a somewhat different formalism as compared to the formalism of Krylov complexity for describing operator growth [50]. This notion finds various applications in the study of chaos, scrambling, and integrability in many-body quantum and semiclassical systems [51,52,[54][55][56][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78].…”

Section: Krylov (Spread) Complexity For Statesmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Néel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such "closeness" by the q-deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Néel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Néel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.

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Section: Krylov (Spread) Complexity For Statesmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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Krylov complexity of deformed conformal field theories

Chattopadhyay,

Malvimat,

Mitra

2024

J. High Energ. Phys.

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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 $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ , $$ \textrm{J}\overline{\textrm{T}} $$ J T ¯ , and $$ \textrm{J}\overline{\textrm{J}} $$ J J ¯ deformations, focusing on first-order corrections in the deformation parameter. Under $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation, we demonstrate that the Lanczos coefficients bn exhibit unexpected behavior, deviating from linear growth within the valid perturbative regime. Notably, the Krylov exponent characterizing the rate of exponential growth of complexity surpasses that of the undeformed theory for positive value of deformation parameter, suggesting a potential violation of the conjectured operator growth bound within the realm of perturbative analysis. One may attribute this to the existence of logarithmic branch points along with higher order poles in the autocorrelation function compared to the undeformed case. In contrast to this, both $$ \textrm{J}\overline{\textrm{J}} $$ J J ¯ and $$ \textrm{J}\overline{\textrm{T}} $$ J T ¯ deformations induce no first order correction to either the linear growth of Lanczos coefficients at large-n or the Krylov exponent and hence the results for these two deformations align with those of the undeformed theory.

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Operator growth and Krylov construction in dissipative open quantum systems

Bhattacharya

Nandy

Nath

et al. 2022

J. High Energ. Phys.

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Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.

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Stability of exponentially damped oscillations under perturbations of the Mori-Chain

Cited by 3 publications

References 21 publications

Probing quantum scars and weak ergodicity breaking through quantum complexity

Probing quantum scars and weak ergodicity breaking through quantum complexity

Krylov complexity of deformed conformal field theories

Operator growth and Krylov construction in dissipative open quantum systems

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