2021
DOI: 10.1103/physreva.103.042414
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Quantum operator growth bounds for kicked tops and semiclassical spin chains

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Cited by 33 publications
(21 citation statements)
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“…Since we directly make an analogy between Heisenberg operator evolution and the dynamics of a "quantum state", this general strategy of bounding commutators has been coined the "many-body quantum walk approach" [13,[19][20][21].…”
Section: 𝑈(𝑛 ' )mentioning
confidence: 99%
See 1 more Smart Citation
“…Since we directly make an analogy between Heisenberg operator evolution and the dynamics of a "quantum state", this general strategy of bounding commutators has been coined the "many-body quantum walk approach" [13,[19][20][21].…”
Section: 𝑈(𝑛 ' )mentioning
confidence: 99%
“…In Einstein's theory of relativity, information cannot travel faster than the speed of light c. However, there can also be emergent speed limits (such as a speed of sound which controls auditory signaling) which are much slower than c. In quantum mechanical systems, it was first proved by Lieb and Robinson [1] that there is a finite speed of quantum information in local lattice models with finite-dimensional Hilbert spaces (on any given site). Especially in recent years, many authors have qualitatively improved upon the original bounds of Lieb and Robinson, both in local lattice models [2][3][4][5][6], in dissipative and non-unitary dynamics [7], models with power-law interactions [8][9][10][11][12][13][14][15][16][17], in all-to-all interacting models [18,19], in semiclassical spin models [6,20], and even in microscopic toy models of quantum gravity [21,22].…”
Section: Introductionmentioning
confidence: 99%
“…The linear growth of b n ∌ an translates to exponential growth of the Kcomplexity, with characteristic Lyapunov exponent λ L = 2a. This operator growth hypothesis has been further studied and verified numerically in various examples [3,20,22,[34][35][36][37][38][39][40][41][42].…”
Section: Jhep12(2021)188mentioning
confidence: 94%
“…The linear growth of b n ∌ an translates to exponential growth of the K-complexity, with characteristic Lyapunov exponent λ L = 2a. This operator growth hypothesis has been further studied and verified numerically in various examples [3,19,21,[33][34][35][36][37][38][39][40][41] .…”
Section: The Ingredients 21 Notions Of Operator Growthmentioning
confidence: 75%