Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu, Shenglong; Swingle, Brian

doi:10.48550/arxiv.2202.07060

Cited by 22 publications

(37 citation statements)

References 129 publications

(188 reference statements)

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“…Recently, barren plateaus were shown to exist when learning random unitaries [11]. These results also extend to learning scramblers [12][13][14][15][16], unitaries which spread local information. This is complemented by an amalgam of results connecting scrambling and QML [17][18][19].…”

Section: Introductionmentioning

confidence: 65%

Barren plateaus from learning scramblers with local cost functions

Garcia¹,

Chen²,

Bu³

et al. 2022

Preprint

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Section: Introductionmentioning

confidence: 65%

Barren plateaus from learning scramblers with local cost functions

Garcia¹,

Chen²,

Bu³

et al. 2022

Preprint

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“…Considering O(0) = X L/2 , we plot ρ( , t) = σ ρ σ ( , t) in Fig. 3, which can be seen as a measure for the outof-time-ordered correlator between operators at sites and L/2 [98]. The emerging light cones in Fig.…”

Section: →mentioning

confidence: 99%

Transport and entanglement growth in long-range random Clifford circuits

Richter¹,

Lunt²,

Pal³

2022

Preprint

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Conservation laws and hydrodynamic transport can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we introduce a class of long-range random Clifford circuits with U(1) symmetry, which act as minimal models for more generic quantum systems and provide an ideal framework to explore this phenomenon. Depending on the exponent α controlling the probability ∝ r −α of gates spanning a distance r, transport in such circuits varies from diffusive to superdiffusive and then to superballistic. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to S(t) ∝ t 1/z , where z is the α-dependent dynamical transport exponent. We explain this finding in terms of the inhibited operator spreading in U(1)-symmetric Clifford circuits, where the emerging light cones are intimately related to the transport behavior and are significantly narrower compared to circuits without conservation law. For sufficiently small α, we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves similarly in circuits with and without conservation law. Our work sheds light on the interplay of transport and entanglement and emphasizes the usefulness of constrained Clifford circuits to explore questions in quantum many-body dynamics.

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“…In chaotic systems, operators are supposed to grow more rapidly than their integrable counterparts. The most sought-after measure that has been used is the out-of-time-ordered-correlator (OTOC) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It uses a probe operator to detect the overlap from the time evolution of the reference operator.…”

Section: Introductionmentioning

confidence: 99%

Krylov complexity in saddle-dominated scrambling

Bhattacharjee,

Cao,

Nandy

et al. 2022

Preprint

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In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle-dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.

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Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Cited by 22 publications

References 129 publications

Barren plateaus from learning scramblers with local cost functions

Barren plateaus from learning scramblers with local cost functions

Transport and entanglement growth in long-range random Clifford circuits

Krylov complexity in saddle-dominated scrambling

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