No abstract

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

We investigate the effect of dissipation from a thermal environment on topological pumping in the periodically-driven Rice-Mele model. We report that dissipation can improve the robustness of pumping quantisation in a regime of finite driving frequencies. Specifically, in this regime, a low-temperature dissipative dynamics can lead to a pumped charge that is much closer to the Thouless quantised value, compared to a coherent evolution. We understand this effect in the Floquet framework: dissipation increases the population of a Floquet band which shows a topological winding, where pumping is essentially quantised. This finding is a step towards understanding a potentially very useful resource to exploit in experiments, where dissipation effects are unavoidable. We consider small couplings with the environment and we use a Bloch-Redfield quantum master equation approach for our numerics: Comparing these results with an exact MPS numerical treatment we find that the quantum master equation works very well also at low temperature, a quite remarkable fact. arXiv:1905.08808v3 [cond-mat.quant-gas]

We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition towards the Mott-insulating phase. By means of a combination of the Time-Dependent Variational Principle and a Tree-Tensor Network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the amplitude of such oscillations is connected to the residual energy, characterizing the creation of defects while crossing the quantum critical point, while their frequency matches the spectral gap in the Mott insulating phase. Our results are relevant for non-equilibrium atomtronic experiments.arXiv:1907.00009v1 [quant-ph]