



01610nas a2200157   4500008004100000245005700041210005600098260001400154520112700168100002001295700002301315700002901338700002301367700002501390856003701415       2022                        eng d00aSimulation Complexity of Many-Body Localized Systems0 aSimulation Complexity of ManyBody Localized Systems  c5/25/20223 a<p>We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.&nbsp;</p>1 aEhrenberg, Adam1 aDeshpande, Abhinav1 aBaldwin, Christopher, L.1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2205.1296701621nas a2200181   4500008004100000245007900041210006900120260001500189490000800204520106600212100001901278700002001297700002001317700001701337700002301354700002501377856003701402       2019                        eng d00aLocality and Heating in Periodically Driven, Power-law Interacting Systems0 aLocality and Heating in Periodically Driven Powerlaw Interacting  c2019/11/120 v1003 a<p>We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α&gt;D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α&gt;2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.&nbsp;</p>1 aTran, Minh, C.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aTitum, Paraj1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/1908.02773