Time evolution of spread complexity and statistics of work done in quantum quenches

Pal, Kuntal; Pal, Kunal; Gill, Ankit; Sarkar, Tapobrata

doi:10.1103/physrevb.108.104311

Cited by 14 publications

(1 citation statement)

References 89 publications

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“…We believe that there are two main reasons. First, Krylov complexity can be applied to any quantum system making it computationally available, at least in principle, for a plethora of different cases including but not limited to condensed matter and many-body systems [13][14][15][16][17], quantum and conformal field theories [3][4][5][18][19][20], open systems [21][22][23][24][25], topological phases of matter [26,27] and many other topics related to aspects of the above and not only [28][29][30][31]. Second, it is related by its construction to inherent properties and characteristic parameters of the system, namely the Hamiltonian and the Hilbert space that it defines.…”

Section: Introductionmentioning

confidence: 99%

Krylov complexity in a natural basis for the Schrödinger algebra

Patramanis,

Sybesma

2024

SciPost Phys. Core

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We investigate operator growth in quantum systems with two-dimensional Schrödinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schrödinger algebra which is characterized by a semi-direct sum structure are complicated. We propose to compute Krylov complexity for this algebra in a natural orthonormal basis, which produces a pentadiagonal structure of the time evolution operator, contrasting the usual tridiagonal Lanczos algorithm outcome. The resulting complexity behaves as expected. We advocate that this approach can provide insights to other non-semisimple algebras.

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Section: Introductionmentioning

confidence: 99%

Krylov complexity in a natural basis for the Schrödinger algebra

Patramanis,

Sybesma

2024

SciPost Phys. Core

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

Bhattacharya,

Das,

Dey

et al. 2024

J. High Energ. Phys.

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Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.

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Spread complexity in saddle-dominated scrambling

Huh,

Jeong,

Pedraza

2024

J. High Energ. Phys.

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Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scrambling. Specifically, we focus on the Lipkin-Meshkov-Glick model and the inverted harmonic oscillator as representative examples of quantum mechanical systems featuring saddle-dominated scrambling. Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of chaotic systems, displaying a distinctive ramp-peak-slope-plateau pattern. Our results indicate that, although spread complexity serves as a valuable probe, accurately diagnosing true quantum chaos generally necessitates additional physical input. We also explore the relationship between spread complexity, the spectral form factor, and the transition probability within the Krylov space. We provide analytical confirmation of our numerical results, validating the Ehrenfest theorem of complexity and identifying a distinct quadratic behavior in the early-time regime of spread complexity.

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Time evolution of spread complexity and statistics of work done in quantum quenches

Cited by 14 publications

References 89 publications

Krylov complexity in a natural basis for the Schrödinger algebra

Krylov complexity in a natural basis for the Schrödinger algebra

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

Spread complexity in saddle-dominated scrambling

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