01565nas a2200169 4500008004100000245004300041210004200084260001400126520108300140100003001223700002001253700002101273700002501294700002101319700001801340856003701358 2021 eng d00aRainbow Scars: From Area to Volume Law0 aRainbow Scars From Area to Volume Law c7/12/20213 a

Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare "scarred" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is sub-extensive. When internal symmetries are present, the construction leads to multiple, and even towers of rainbow scars revealed through distinctive non-thermal dynamics. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system. 

1 aLanglett, Christopher, M.1 aYang, Zhi-Cheng1 aWildeboer, Julia1 aGorshkov, Alexey, V.1 aIadecola, Thomas1 aXu, Shenglong uhttps://arxiv.org/abs/2107.0341601785nas a2200145 4500008004100000245005600041210005600097260001100153300001200164490000700176520138200183100001801565700001901583856003701602 2020 eng d00aAccessing scrambling using matrix product operators0 aAccessing scrambling using matrix product operators c2/2020 a199-2040 v163 a

Scrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. In this work, we present a general method to calculate OTOCs of local operators in local one-dimensional systems based on approximating Heisenberg operators as matrix-product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with 201 sites. Based on this data and OTOC results for black holes, local random circuit models, and non-interacting systems, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than fifteen orders of magnitude.

1 aXu, Shenglong1 aSwingle, Brian uhttps://arxiv.org/abs/1802.0080101122nas a2200169 4500008004100000245008500041210007000126260001300196490000800209520061300217100001700830700001800847700001500865700001600880700001900896856003700915 2020 eng d00aThe operator Lévy flight: light cones in chaotic long-range interacting systems0 aoperator Lévy flight light cones in chaotic longrange interactin c7/6/20200 v1243 a

We propose a generic light cone phase diagram for chaotic long-range r−α interacting systems, where a linear light cone appears for α≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the Lévy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites. 

1 aZhou, Tianci1 aXu, Shenglong1 aChen, Xiao1 aGuo, Andrew1 aSwingle, Brian uhttps://arxiv.org/abs/1909.0864601875nas 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/2008.0230301902nas a2200157 4500008004100000245011500041210006900156260001500225520137700240100001801617700001301635700001701648700001901665700002301684856003701707 2019 eng d00aButterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization0 aButterfly effect in interacting AubryAndre model thermalization  c02/19/20193 a

The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.

1 aXu, Shenglong1 aLi, Xiao1 aHsu, Yi-Ting1 aSwingle, Brian1 aSarma, Sankar, Das uhttps://arxiv.org/abs/1902.0719901967nas a2200133 4500008004100000245005100041210004900092260001400141490000600155520159800161100001801759700001901777856003701796 2019 eng d00aLocality, Quantum Fluctuations, and Scrambling0 aLocality Quantum Fluctuations and Scrambling c9/18/20190 v93 a

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

1 aXu, Shenglong1 aSwingle, Brian uhttps://arxiv.org/abs/1805.0537601664nas 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