Effective models for gapped phases of strongly correlated quantum lattice models

We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.Comment: 6 pages, 5 figures, extended discussion on J2/J1 for the honeycomb Hubbard model and on the properties of different generators for the continuous unitary transformatio

Cascades of Dynamical Transitions in an Adaptive Population

In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical transitions from vanishing to non-vanishing step sizes. When the diversity decreases further, we find a cascade of dynamical transitions for the different signal dimensions, supported by good agreement between simulations and theory. Besides, the signal of the largest step size at the steady state is likely to be the initial signal.Comment: 4 pages, 8 figure

The Impact of Radio AGN Bubble Composition on the Dynamics and Thermal Balance of the Intracluster Medium

Feeding and feedback of active galactic nuclei (AGN) are critical for understanding the dynamics and thermodynamics of the intracluster medium (ICM) within the cores of galaxy clusters. While radio bubbles inflated by AGN jets could be dynamically supported by cosmic rays (CRs), the impact of CR-dominated jets are not well understood. In this work, we perform three-dimensional simulations of CR-jet feedback in an isolated cluster atmosphere; we find that CR jets impact the multiphase gas differently than jets dominated by kinetic energy. In particular, CR bubbles can more efficiently uplift the cluster gas and cause an outward expansion of the hot ICM. Due to adiabatic cooling from the expansion and less efficient heating from CR bubbles by direct mixing, the ICM is more prone to local thermal instabilities, which will later enhance chaotic cold accretion onto the AGN. The amount of cold gas formed during the bubble formation and its late-time evolution sensitively depend on whether CR transport processes are included or not. We also find that low-level, subsonic driving of turbulence by AGN jets holds for both kinetic and CR jets; nevertheless, the kinematics is consistent with the Hitomi measurements. Finally, we carefully discuss the key observable signatures of each bubble model, focusing on gamma-ray emission (and related comparison with Fermi), as well as thermal Sunyaev-Zel'dovich constraints.Comment: accepted to Ap

The Fermi Bubbles: Gamma-ray, Microwave, and Polarization Signatures of Leptonic AGN Jets

The origin of the Fermi bubbles and the microwave haze is yet to be determined. To disentangle different models requires detailed comparisons between theoretical predictions and multi-wavelength observations. Our previous simulations have demonstrated that the primary features of the Fermi bubbles could be successfully reproduced by recent jet activity from the central active galactic nucleus (AGN). In this work, we generate gamma-ray and microwave maps and spectra based on the simulated properties of cosmic rays (CRs) and magnetic fields in order to examine whether the observed bubble and haze emission could be explained by leptons contained in the AGN jets. We also investigate the model predictions of the polarization properties of the Fermi bubbles. We find that: (1) The same population of leptons can simultaneously explain the bubble and haze emission given that the magnetic fields within the bubbles are very close to the exponentially distributed ambient field, which can be explained by mixing in of the ambient field followed by turbulent field amplification; (2) The centrally peaked microwave profile suggests CR replenishment, which is consistent with the presence of a more recent second jet event; (3) The bubble interior exhibits a high degree of polarization because of ordered radial magnetic field lines stretched by elongated vortices behind the shocks; highly-polarized signals could also be observed inside the draping layer; (4) Enhancement of rotation measures could exist within the shock-compressed layer because of increased gas density and more amplified and ordered magnetic fields. We discuss the possibility that the deficient haze emission at b<-35 degrees is due to the suppression of magnetic fields, which is consistent with the existence of lower-energy CRs causing the polarized emission at 2.3 GHz. Possible AGN jet composition in the leptonic scenario is also discussed.Comment: 15 pages, 9 figures, matched with MNRAS published versio

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.Comment: 4 pages, 4 figures, published versions with additional dat