A homogeneous polarized dipolar Bose-Einstein condensate is considered in the presence of weak quenched disorder within mean-field theory at zero temperature. By first solving perturbatively the underlying Gross-Pitaevskii equation and then performing disorder ensemble averages for physical observables, it is shown that the anisotropy of the two-particle interaction is passed on to both the superfluid density and the sound velocity.

Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such non-local fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this work, we propose a way to overcome this challenge. We suggest a method intertwining the optimisation over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalises basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimisation in tensor network methods.Capturing strongly correlated quantum systems is one of the major challenges of modern theoretical and computational physics. Recent years have seen a surge of interest in the development of potent numerical methods based on tensor networks to approximate ground states of interacting lattice models [1][2][3][4][5][6][7], building upon the success of the density-matrix renormalisation group (DMRG) [1]. It has become clear that such ideas are also applicable to fermionic systems [8][9][10], and even to systems of quantum chemistry [11][12][13][14][15][16][17][18][19], lacking the locality present in lattice models in condensed-matter systems. Such tools allow in principle to approximate the full configuration interaction solution to good accuracy with reasonable effort, going in instances beyond conventional approaches to quantum chemistry, such as coupled cluster [20], configuration interaction or density-functional theory [21,22], as convincingly shown by first implementations of DMRG algorithms in quantum chemistry (QC-DMRG) [11][12][13][14][15].Yet, there is a new obstacle to be overcome: Tensor network methods have originally been tailored to capture local interactions, and consequently ground states exhibiting shortrange correlations and entanglement area laws [7]. Systems in quantum chemistry pose new challenges due to the inherent long-ranged interactions, which are present no matter in what basis the systems are expressed. New questions hence arise concerning the optimal topology and physical (orbital) basis used to construct the tensor network state [13][14][15][16][17][18][19][23][24][25].In this work, we propose a novel approach towards making use of tensor network methods in quantum chemistry, by suggesting an adaptive scheme of updating basis transformations "on the fly" in conjunction with tensor network updates. In this way, we bring together advantages of matrix product states -which can capture strongly correlated states, but are tailored to short-ranged correlations and low entanglement -and fermionic Gaussian mode transformations -for which entanglement is no obstacle, but non-Gaussian correlations are. We hence go significantly beyond previous approaches towards optimising fermionic base...

In this work, we present a result on the non-equilibrium dynamics causing equilibration and Gaussification of quadratic non-interacting fermionic Hamiltonians. Specifically, based on two basic assumptions -clustering of correlations in the initial state and the Hamiltonian exhibiting delocalizing transport -we prove that nonGaussian initial states become locally indistinguishable from fermionic Gaussian states after a short and well controlled time. This relaxation dynamics is governed by a power-law independent of the system size. Our argument is general enough to allow for pure and mixed initial states, including thermal and ground states of interacting Hamiltonians on and large classes of lattices as well as certain spin systems. The argument gives rise to rigorously proven instances of a convergence to a generalized Gibbs ensemble. Our results allow to develop an intuition of equilibration that is expected to be more generally valid and relates to current experiments of cold atoms in optical lattices.Despite the great complexity of quantum many-body systems out-of-equilibrium, local expectation values in such systems show the remarkable tendency to equilibrate to stationary values that do not depend on the microscopic details of the initial state, but rather can be described with few parameters using thermal states or generalized Gibbs ensembles [1][2][3]. Such behavior has been successfully studied in many settings theoretically and experimentally, most notably in instances of quantum simulations in optical lattices [2,4,5].By now, it is clear that, despite the unitary nature of quantum mechanical evolution, local expectation values equilibrate due to a dephasing between the eigenstates [3,[6][7][8][9][10][11]. So far it is, however, unclear why this dephasing tends to happen so rapidly. In fact, experiments often observe equilibration after very short times which are independent of the system size [5,12], while even the best theoretical bounds for general initial states of concrete systems diverge exponentially [2,11]. This discrepancy poses the challenge of precisely identifying the equilibration time, which constitutes one of the main open questions in the field [1][2][3].What is more, only little is known about how exactly the equilibrium expectation values emerge. Due to the exponentially many constants of motion present in quantum manybody systems, corresponding to the overlaps with the eigenvectors of the system, there seems to be no obvious reason why equilibrium values often only depend on few macroscopic properties such as temperature or particle number. In short: It is unclear how precisely the memory of the initial conditions is lost during time evolution.To make progress towards a solution of these two problems, it is instructive to study the behavior of non-interacting particles captured by so-called quadratic or free models. In these models the time evolution of so called Gaussian states, which are fully described by their correlation matrix, is particularly simple to describe. While studying...

One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasi-local unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish a new approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder. arXiv:1707.05181v3 [cond-mat.stat-mech]

Quantum simulators allow to explore static and dynamical properties of otherwise intractable quantum manybody systems. In many instances, however, it is the read-out that limits such quantum simulations. In this work, we introduce a new paradigm of experimental read-out exploiting coherent non-interacting dynamics in order to extract otherwise inaccessible observables. Specifically, we present a novel tomographic recovery method allowing to indirectly measure second moments of relative density fluctuations in one-dimensional superfluids which until now eluded direct measurements. We achieve this by relating second moments of relative phase fluctuations which are measured at different evolution times through known dynamical equations arising from unitary non-interacting multi-mode dynamics. Applying methods from signal processing we reconstruct the full matrix of second moments, including the relative density fluctuations. We employ the method to investigate equilibrium states, the dynamics of phonon occupation numbers and even to predict recurrences. The method opens a new window for quantum simulations with one-dimensional superfluids, enabling a deeper analysis of their equilibration and thermalization dynamics.Quantum simulators offer entirely new perspectives of assessing the intriguing physics of quantum many-body systems in and out of equilibrium. They are experimental setups allowing to probe properties of complex quantum systems under unprecedented levels of control [1][2][3], beyond the possibilities of classical simulations. Among other platforms, experiments with ultra-cold atoms involving large particle numbers or even continuous quantum fields have been particularly insightful [4][5][6][7][8][9][10][11][12][13][14].And yet, key questions remain open for a highly unexpected reason: The read-out of state-of-the-art quantum simulators is limited. In one-dimensional superfluids, for example, one can probe the dynamics of equilibration [4] occurring in the presence of an effective light-cone [5] and leading to generalized Gibbs ensembles [6]. The excellent experimental control over that system allowed to observe coherent recurrences in the dynamics of a system of thousands of atoms [8]. However, in that particular setup, further quantifying the recent observations is currently obstructed because only phase quadratures but not canonically conjugate density fluctuations can be measured. On the contrary, if both quadratures could be measured, and hence if genuine quantum read-out was possible, then studies of intricate questions on the role of interactions, or entanglement dynamics after a quench could become possible.This situation is by no means an exception: In fact, in any quantum simulation platform, read-out prescriptions are always restricted in one way or another which constitutes a crucial bottleneck towards studying intricate physical questions. For cold atoms in optical lattices, akin to the development which will be laid out in this work, innovations such as the quantum gas microscope [15][16][17...