Front dynamics and entanglement in the XXZ chain with a gradient

We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.Comment: 14 pages, 6 figures, minor changes, as publishe

Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multi-dimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitudes. A core concept of QQMC is the a priori construction of a "model function" that approximates the integrand and is used to optimize the sampling distribution. In this paper, we show that the model function concept extends to a kernel approach for the computation of Green functions. We illustrate the approach on the Anderson impurity model and show that the scaling of the error with the number of integrand evaluations $N$ is $\sim 1/N^{0.86}$ in the best cases, and comparable to Monte Carlo scaling $\sim 1/N^{0.5}$ in the worst cases. We find a systematic improvement over Monte Carlo sampling by at least two orders of magnitude while using a basic form of model function. Finally, we compare QQMC results with calculations performed with the Fork Tensor Product State (FTPS) method, a recently developed tensor network approach for solving impurity problems. Applying a simple Pad\'e approximant for the series resummation, we find that QQMC matches the FTPS results beyond the perturbative regime.Comment: 18 pages, 11 figure

AIM2 recognizes cytosolic dsDNA and forms a caspase-1-activating inflammasome with ASC

The innate immune system senses nucleic acids by germline-encoded pattern recognition receptors. RNA is sensed by Toll-like receptor members TLR3, TLR7 and TLR8, or by the RNA helicases RIG-I (also known as DDX58) and MDA-5 (IFIH1). Little is known about sensors for cytoplasmic DNA that trigger antiviral and/or inflammatory responses. The best characterized of these responses involves activation of the TANK-binding kinase (TBK1)-interferon regulatory factor 3 (IRF3) signalling axis to trigger transcriptional induction of type I interferon genes. A second, less well-defined pathway leads to the activation of an 'inflammasome' that, via caspase-1, controls the catalytic cleavage of the pro-forms of the cytokines IL1beta and IL18 (refs 6, 7). Using mouse and human cells, here we identify the PYHIN (pyrin and HIN domain-containing protein) family member absent in melanoma 2 (AIM2) as a receptor for cytosolic DNA, which regulates caspase-1. The HIN200 domain of AIM2 binds to DNA, whereas the pyrin domain (but not that of the other PYHIN family members) associates with the adaptor molecule ASC (apoptosis-associated speck-like protein containing a caspase activation and recruitment domain) to activate both NF-kappaB and caspase-1. Knockdown of Aim2 abrogates caspase-1 activation in response to cytoplasmic double-stranded DNA and the double-stranded DNA vaccinia virus. Collectively, these observations identify AIM2 as a new receptor for cytoplasmic DNA, which forms an inflammasome with the ligand and ASC to activate caspase-1

A real-frequency solver for the Anderson impurity model based on bath optimization and cluster perturbation theory

Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites ($\approx 50$). Then, the bath is optimized by unitary transformations such that it separates into two parts that are weakly coupled. One part contains the impurity site and its interacting Green's functions can be determined with ED. The other (larger) part is a non-interacting system containing all the remaining bath sites. Finally, the Green's function of the full AIM is calculated via coupling these two parts with cluster perturbation theory.Comment: 5 pages, 4 figures, SCES 2017 Proceeding

Time dependent variational principle for tree Tensor Networks

We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spin-orbit coupling effects are important, or when distortions of the crystal lattice are present.Comment: Submission to SciPos