29 research outputs found
Equilibration via Gaussification in fermionic lattice systems
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 non-Gaussian 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.Comment: 5+15 pages, 3 figures, presentation improve
Construction of exact constants of motion and effective models for many-body localized systems
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- 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.Comment: 8 pages, 8 figures, replaced with published versio
Composite symmetry protected topological order and effective models
Strongly correlated quantum many-body systems at low dimension exhibit a
wealth of phenomena, ranging from features of geometric frustration to
signatures of symmetry-protected topological order. In suitable descriptions of
such systems, it can be helpful to resort to effective models which focus on
the essential degrees of freedom of the given model. In this work, we analyze
how to determine the validity of an effective model by demanding it to be in
the same phase as the original model. We focus our study on one-dimensional
spin-1/2 systems and explain how non-trivial symmetry protected topologically
ordered (SPT) phases of an effective spin 1 model can arise depending on the
couplings in the original Hamiltonian. In this analysis, tensor network methods
feature in two ways: On the one hand, we make use of recent techniques for the
classification of SPT phases using matrix product states in order to identify
the phases in the effective model with those in the underlying physical system,
employing Kuenneth's theorem for cohomology. As an intuitive paradigmatic model
we exemplify the developed methodology by investigating the bi-layered
delta-chain. For strong ferromagnetic inter-layer couplings, we find the system
to transit into exactly the same phase as an effective spin 1 model. However,
for weak but finite coupling strength, we identify a symmetry broken phase
differing from this effective spin-1 description. On the other hand, we
underpin our argument with a numerical analysis making use of matrix product
states.Comment: 13 pages, 6 figure
Quantum read-out for cold atomic quantum simulators
Quantum simulators allow to explore static and dynamical properties of otherwise intractable quantum many-body systems. In many instances, however, the read-out limits such quantum simulations. In this work, we introduce an innovative experimental read-out exploiting coherent non-interacting dynamics. Specifically, we present a tomographic recovery method allowing to indirectly measure the second moments of the relative density fluctuations between two one-dimensional superfluids, which until now eluded direct measurements. Applying methods from signal processing, we show that we can reconstruct the relative density fluctuations from non-equilibrium data of the relative phase 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
Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder
The effect of a weak three-dimensional (3d) isotropic laser speckle disorder
on various thermodynamic properties of a dilute Bose gas is considered at zero
temperature. First, we summarize the derivation of the autocorrelation function
of laser speckles in 1d and 2d following the seminal work of Goodman. The goal
of this discussion is to show that a Gaussian approximation of this function,
proposed in some recent papers, is inconsistent with the general background of
laser speckle theory. Then we propose a possible experimental realization for
an isotropic 3d laser speckle potential and derive its corresponding
autocorrelation function. Using a Fourier transform of that function, we
calculate both condensate depletion and sound velocity of a Bose-Einstein
condensate as disorder ensemble averages of such a weak laser speckle potential
within a perturbative solution of the Gross-Pitaevskii equation. By doing so,
we reproduce the expression of the normalfluid density obtained earlier within
the treatment of Landau. This physically transparent derivation shows that
condensate particles, which are scattered by disorder, form a gas of
quasiparticles which is responsible for the normalfluid component