Product spectrum ansatz and the simplicity of thermal states

Martyn, John M.; Swingle, Brian

doi:10.1103/physreva.100.032107

Cited by 76 publications

(73 citation statements)

References 57 publications

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“…How can we extend our bound on chaos to finite T ? Numerical investigations into these questions are challenging due to the presence of the thermal density matrix [22,93,94]. Quantum Monte Carlo seems promising for this problem, as the Lanczos coefficients can be computed without analytic continuation.…”

Section: B Outlookmentioning

confidence: 99%

A Universal Operator Growth Hypothesis

et al. 2019

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We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate α in generic systems, with an extra logarithmic correction in 1d. The rate α -an experimental observable -governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-N limits. Moreover, α upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents λL ≤ 2α, which complements and improves the known universal low-temperature bound λL ≤ 2πT . We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants. CONTENTS

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Section: B Outlookmentioning

confidence: 99%

A Universal Operator Growth Hypothesis

et al. 2019

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“…Since we are interested in real-time dynamics of the SD equations, we work in real frequency ω and time t. To obtain the relevant retarded propagators we apply the standard analytical continuation iω n → ω + iδ to Eqs. (31) and write…”

Section: Appendix A: Tfd Preparation At Negative Timesmentioning

confidence: 99%

“…2a). We also note interesting recent works on how to prepare a TFD state using quantum circuits [30][31][32]; however, these approaches are limited to the moderate system sizes accessible on present-day quantum simulators, similar to the experiments of Refs. [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Lantagne-Hurtubise

Plugge

Can

et al. 2020

Phys. Rev. Research

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Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however in most interacting many-body systems, this is not a viable option. Here we propose a new family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of the system. We show that, remarkably, in this situation the Lyapunov chaos exponent λL can be extracted from the measurement of an ordinary two-point correlation function. As an unexpected bonus, we find that our proposed method yields the so-called "regularized" OTOC -a quantity that is believed to most directly indicate quantum chaos. According to recent theoretical work, the TFD state can be prepared as the ground state of two weakly coupled identical systems and is therefore amenable to experimental study. We illustrate the utility of these protocols on the example of the maximally chaotic Sachdev-Ye-Kitaev model and support our findings by extensive numerical simulations.

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“…Details on how to create this state are given in [8][9][10]. The entanglement is the key resource for quantum teleportation, geometrically it builds the connected wormhole geometry [26].…”

Section: Gao-jafferis-wall Wormholementioning

confidence: 99%

“…(3.79) 10 Notice that this equation is only valid for d > 2. Moreover, in the case d = 3 the polynomial reduces to a logarithm, |x| 3−d → log |x|.…”

Section: Generalization To D + 1 Dimensionsmentioning

confidence: 99%

Traversable wormholes in AdS and bounds on information transfer

Freivogel

Galante

Nikolakopoulou

et al. 2020

J. High Energ. Phys.

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We analyze the amount of information that can be sent through the traversable wormholes of Gao, Jafferis, and Wall. Although we find that the wormhole is open for a proper time shorter than the Planck time, the transmission of a signal through the wormhole can sometimes remain within the semiclassical regime. For black holes with horizons of order the AdS radius, information cannot be reliably sent through the wormhole. However, black holes with horizon radius much larger than the AdS radius do allow for the transmission of a number of quanta of order the horizon area in AdS units. More information can be sent through the wormhole by increasing the number of light fields contributing to the negative energy. Our bulk computations agree with a boundary analysis based on quantum teleportation.

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Product spectrum ansatz and the simplicity of thermal states

Cited by 76 publications

References 57 publications

A Universal Operator Growth Hypothesis

A Universal Operator Growth Hypothesis

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Traversable wormholes in AdS and bounds on information transfer

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