New BCH-like relations of the su(1,1), su(2) and so(2,1) Lie algebras

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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“…Let us now note the following relations [111]. For an operator given by Ĝ = e λ + T + +λ − T − +λ 0 T 0 +ω1 , (A4)…”

Section: Appendix A: Complexity For Su(2) Symmetrymentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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“…However, both operators of Eqs. ( 28) and ( 30) can be identified as elements of the su(1, 1) Lie algebra and, therefore, we can use new BCH-like relations [63] to calculate their product as…”

Section: Time Evolutionmentioning

confidence: 99%

“…Then, in order to identify and clarify some subtleties and usual inaccuracies in the literature, we also describe the system in the basis that diagonalizes the hamiltonian at any time. The aforementioned bases are related by Bogoliubov transformations and we do explicit calculations for the basis transformation using new BCH-like relations [63]. We discuss squeezing and adiabaticity relative to each basis and to different quadrature operators.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

Martínez-Tibaduiza,

Pires,

Farina

2020

Preprint

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“…Historically, DCOSHO was used in order to derive quantum solutions of harmonic oscillators with time-varying parameters as well as the simple harmonic oscillator. For instance, Tibaduiza et al derived quantum algebraic solutions for nonstationary harmonic oscillators using Lie algebraic approach based on DCOSHO 21 , 22 .…”

Section: Introductionmentioning

confidence: 99%

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

Choi

2022

Sci Rep

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The characteristics of nonextensivity for a general quantum dissipative oscillatory system in the SU(1,1) coherent states are investigated using the invariant operator method. We consider a deformed Caldirola-Kanai oscillator represented in terms of a parameter q which is a measure of the degree of nonextensivity. The nonextensivity effects on the parametric evolution of the SU(1,1) coherent states are elucidated. We compare our results with those of previous researches and address the advantage of our methodology which adopts the linear invariant operator. In particular, the nonextensive behaviors associated with the fluctuations of canonical variables and the dissipation of quantum energy are analyzed in detail regarding their dependence on q. The properties of SU(1,1) coherent states that we adopt here can be utilized in quantum-information processes such as cloning, swapping, and teleportation of state information.

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New BCH-like relations of the su(1,1), su(2) and so(2,1) Lie algebras

Cited by 11 publications

References 22 publications

Probing quantum scars and weak ergodicity breaking through quantum complexity

Probing quantum scars and weak ergodicity breaking through quantum complexity

Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

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