01875nas a2200145 4500008004100000245004100041210003900082260001300121520148600134100001801620700002201638700001301660700001901673856003701692 2020 eng d00aA Sparse Model of Quantum Holography0 aSparse Model of Quantum Holography c8/5/20203 a

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, k, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed k. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when k is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.

1 aXu, Shenglong1 aSusskind, Leonard1 aSu, Yuan1 aSwingle, Brian uhttps://arxiv.org/abs/2008.0230301664nas a2200157 4500008004100000245006600041210006200107260001500169520119400184100001801378700001901396700001701415700001901432700001801451856003701469 2019 eng d00aThe Speed of Quantum Information Spreading in Chaotic Systems0 aSpeed of Quantum Information Spreading in Chaotic Systems c08/19/20193 a

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.

1 aCouch, Josiah1 aEccles, Stefan1 aNguyen, Phuc1 aSwingle, Brian1 aXu, Shenglong uhttps://arxiv.org/abs/1908.0699301302nas a2200121 4500008004100000245008600041210006900127520089100196100001901087700001801106700001901124856003701143 2018 eng d00aScrambling dynamics across a thermalization-localization quantum phase transition0 aScrambling dynamics across a thermalizationlocalization quantum 3 a

We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.

1 aSahu, Subhayan1 aXu, Shenglong1 aSwingle, Brian uhttps://arxiv.org/abs/1807.06086