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A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison of ML-MCTDH with the discrete truncated Wigner approximation (DTWA) demonstrates that our approach excels in handling anisotropic models and consistently provides better results for two-point observables in all simulation instances. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this paper, we employ a numerical technique referred to as multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multilayering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

We employ the multiconfiguration time-dependent Hartree method for bosons in order to investigate the correlated nonequilibrium quantum dynamics of two bosons confined in two colliding and uniformly accelerated Gaussian wells. As the wells approach each other an effective, transient double-well structure is formed. This induces a transient and oscillatory over-barrier transport. We monitor both the amplitude of the intrawell dipole mode in the course of the dynamics as well as the final distribution of the particles between the two wells. For fast collisions we observe an emission process which we attribute to two distinct mechanisms. Energy transfer processes lead to an untrapped fraction of bosons and a resonant enhancement of the deconfinement for certain kinematic configurations can be observed. Despite the comparatively weak interaction strengths employed in this work, we identify strong interparticle correlations by analyzing the corresponding von Neumann entropy.

The investigation of the nonequilibrium quantum dynamics of bosonic many-body systems is very challenging due to the excessively growing Hilbert space and poses a major problem for their theoretical description and simulation. We present a novel dynamical pruning approach in the framework of the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) to tackle this issue by dynamically detecting the most relevant number states of the underlying physical system and modifying the many-body Hamiltonian accordingly. We discuss two different number state selection criteria as well as two different ways to modify the Hamiltonian. Our scheme regularly re-evaluates the number state selection in order to dynamically adapt to the time evolution of the system. To benchmark our methodology, we study the nonequilibrium dynamics of bosonic particles confined either in an optical lattice or in a double-well potential. It is shown that our approach reproduces the unpruned MCTDHB results accurately while yielding a significant reduction of the simulation time. The speedup is particularly pronounced in the case of the optical lattice.