6 research outputs found
Finite time large deviations via matrix product states
Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamical observables at arbitrary finite time. This is a harder problem because, in contrast to the infinite time case where only the extremal eigenstate of a tilted Markov generator is relevant, for finite time the whole spectrum plays a role. We show that finite time dynamical partition sums can be computed efficiently and accurately in one dimension using matrix product states, and describe how to use such results to generate rare event trajectories on demand. We apply our methods to the Fredrickson-Andersen (FA) and East kinetically constrained models, and to the symmetric simple exclusion process (SSEP), unveiling dynamical phase diagrams in terms of counting field and trajectory time. We also discuss extensions of this method to higher dimensions
Investigation of the 1+1 dimensional Thirring model using the method of matrix product states
We present preliminary results of a study on the non-thermal phase structure
of the (1+1) dimensional massive Thirring model, employing the method of matrix
product states. Through investigating the entanglement entropy, the fermion
correlators and the chiral condensate, it is found that this approach enables
us to observe numerical evidence of a Kosterlitz-Thouless phase transition in
the model.Comment: 7 pages, 4 figures; contribution to the proceedings of Lattice 2018
conferenc
Single-site- and single-atom-resolved measurement of correlation functions
Correlation functions play an important role for the theoretical and
experimental characterization of many-body systems. In solid-state systems,
they are usually determined through scattering experiments whereas in
cold-gases systems, time-of-flight and in-situ absorption imaging are the
standard observation techniques. However, none of these methods allow the
in-situ detection of spatially resolved correlation functions at the
single-particle level. Here we give a more detailed account of recent advances
in the detection of correlation functions using in-situ fluorescence imaging of
ultracold bosonic atoms in an optical lattice. This method yields single-site
and single-atom-resolved images of the lattice gas in a single experimental
run, thus gaining direct access to fluctuations in the many-body system. As a
consequence, the detection of correlation functions between an arbitrary set of
lattice sites is possible. This enables not only the detection of two-site
correlation functions but also the evaluation of non-local correlations, which
originate from an extended region of the system and are used for the
characterization of quantum phases that do not possess (quasi-)long-range order
in the traditional sense.Comment: extended version of M. Endres et al., Science 334, 200-203 (2011)
[arXiv:1108.3317
A quantum information perspective on meson melting
We propose to use quantum information notions to characterize thermally induced melting of nonperturbative bound states at high temperatures. We apply tensor networks to investigate this idea in static and dynamical settings within the Ising quantum field theory, where bound states are confined fermion pairs - mesons. In equilibrium, we identify the transition from an exponential decay to a power law scaling with temperature in an efficiently computable second Renyi entropy of a thermal density matrix as a signature of meson melting. Out of equilibrium, we identify as the relevant signature the transition from an oscillatory to a linear growing behavior of reflected entropy after a thermal quench. These analyses apply more broadly, which brings new ways of describing in-medium meson phenomena in quantum many-body and high-energy physics
Almost conserved operators in nearly many-body localized systems
We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slowoperators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase