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Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems. The nonequilibrium properties of many-body systems can be described by the dynamics of the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time simulations. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. The proposed framework utilizes RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. This new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$, where $N_t$ is the total time steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through different numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity transformed Hamiltonians (coupled cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single particle density matrix. The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate by improve significantly upon the mean-field results in the strongly driven regime., Comment: 11 pages, 2 figures in main text. 11 page supplemental information with 6 figures

Quantum point contacts (QPCs) are an essential component in mesoscopic devices. Here, we study the transmission of quantum Hall edge modes through a gate-defined QPC in monolayer graphene. We observe resonant tunneling peaks and a nonlinear conductance pattern characteristic of Coulomb-blockaded localized states. The in-plane electric polarizability reveals the states are localized at a classically-unstable electrostatic saddle point. We explain this unexpected finding within a self-consistent Thomas-Fermi model, finding that localization of a zero-dimensional state at the saddle point is favored whenever the applied confinement potential is sufficiently soft compared to the Coulomb energy. Our results provide a direct demonstration of Coulomb-driven reconstruction at the boundary of a quantum Hall system., Comment: 15 pages, 10 figures. arXiv admin note: text overlap with arXiv:2204.10296

In this paper, we propose using LSTM-RNNs (Long Short-Term Memory-Recurrent Neural Networks) to learn and represent nonlinear integral operators that appear in nonlinear integro-differential equations (IDEs). The LSTM-RNN representation of the nonlinear integral operator allows us to turn a system of nonlinear integro-differential equations into a system of ordinary differential equations for which many efficient solvers are available. Furthermore, because the use of LSTM-RNN representation of the nonlinear integral operator in an IDE eliminates the need to perform a numerical integration in each numerical time evolution step, the overall temporal cost of the LSTM-RNN-based IDE solver can be reduced to $O(n_T)$ from $O(n_T^2)$ if a $n_T$-step trajectory is to be computed. We illustrate the efficiency and robustness of this LSTM-RNN-based numerical IDE solver with a model problem. Additionally, we highlight the generalizability of the learned integral operator by applying it to IDEs driven by different external forces. As a practical application, we show how this methodology can effectively solve the Dyson's equation for quantum many-body systems.

The generalized Kadanoff-Baym ansatz (GKBA) is an approximation to the Kadanoff-Baym equations (KBE), that neglects certain memory effects that contribute to the Green's function at non-equal times. Here we present arguments and numerical results to demonstrate the practical insignificance of the quantities neglected when deriving the GKBA at conditions at which KBE and GKBA are appropriate. We provide a mathematical proof that places a scaling bound on the neglected terms, further reinforcing that these terms are typically small in comparison to terms that are kept in the GKBA. We perform calculations in a range of models, including different system sizes and filling fractions, as well as experimentally relevant non-equilibrium excitations. We find that both the GKBA and KBE capture the dynamics of interacting systems with moderate and even strong interactions well. We explicitly compute terms neglected in the GKBA approximation and show, in the scenarios tested here, that they are orders of magnitude smaller than the terms that are accounted for, i.e., they offer only a small correction when included in the full Kadanoff-Baym equations., Comment: 14 pages, 3 figures, Supplemental information with 10 figures

The HF-GKBA offers an approximate numerical procedure for propagating the two-time non-equilibrium Green's function(NEGF). Here we compare the HF-GKBA to exact results for a variety of systems with long and short-range interactions, different two-body interaction strengths and various non-equilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. This agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, look at the use of dynamical mode decomposition(DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16\% of the total time evolution we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long time trajectories in large-scale systems.

In an all-van der Waals heterostructure, the active layer, gate dielectrics and gate electrodes are assembled from two-dimensional crystals that have a low density of atomic defects. This design allows two-dimensional electron systems with very low disorder to be created, particularly in heterostructures where the active layer also has intrinsically low disorder, such as crystalline graphene layers or metal dichalcogenide heterobilayers. A key missing ingredient has been nanoscale electrostatic control, with existing methods for fabricated local gates typically introducing unwanted contamination. Here we describe a resist-free local anodic oxidation process for patterning sub 100nm features in graphite gates, and their subsequent integration into an all-van der Waals heterostructure. We define a quantum point contact in the fractional quantum Hall regime as a benchmark device and observe signatures of chiral Luttinger liquid behaviour, indicating an absence of extrinsic scattering centres in the vicinity of the point contact. In the integer quantum Hall regime, we demonstrate in situ control of the edge confinement potential, a key requirement for the precision control of chiral edge states. This technique may enable the fabrication of devices capable of single anyon control and coherent edge-state interferometry in the fractional quantum Hall regime., Comment: Main Text: 11 pages, 4 figures | Extended Data: 4 figures | Supplementary Info: 6 pages, 4 figures; updated manuscript post review