



01944nas a2200181   4500008004100000245006800041210006700109260001400176520137900190100002201569700001801591700001801609700002401627700002801651700002101679700002501700856003701725       2021                        eng d00aDiscovering hydrodynamic equations of many-body quantum systems0 aDiscovering hydrodynamic equations of manybody quantum systems  c11/3/20213 a<p>Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.</p>1 aKharkov, Yaroslav1 aShtanko, Oles1 aSeif, Alireza1 aBienias, Przemyslaw1 aVan Regemortel, Mathias1 aHafezi, Mohammad1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2111.0238501656nas a2200157   4500008004100000245008100041210006900122260001500191520114900206100002801355700001701383700001801400700002201418700002101440856003701461       2020                        eng d00aEntanglement entropy scaling transition under competing monitoring protocols0 aEntanglement entropy scaling transition under competing monitori  c08/19/20203 a<p>Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second one destroys the coherence via dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides novel insights into the occurrence of a measurement-induced phase transition within a continuous monitoring protocol.</p>1 aVan Regemortel, Mathias1 aCian, Ze-Pei1 aSeif, Alireza1 aDehghani, Hossein1 aHafezi, Mohammad  uhttps://arxiv.org/abs/2008.08619