Extraordinary absorption of decorated undoped graphene

We theoretically study absorption by an undoped graphene layer decorated with arrays of small particles. We discuss periodic and random arrays within a common formalism, which predicts a maximum absorption of $50\%$ for suspended graphene in both cases. The limits of weak and strong scatterers are investigated and an unusual dependence on particle-graphene separation is found and explained in terms of the effective number of contributing evanescent diffraction orders of the array. Our results can be important to boost absorption by single layer graphene due to its simple setup with potential applications to light harvesting and photodetection based on energy (F\"orster) rather than charge transfer.Comment: 5 pages, 3 figure

Faster Methods for Contracting Infinite 2D Tensor Networks

We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published under the name V. Zaune

Disorder and interaction effects in two dimensional graphene sheets

The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points where the strength of the interactions remains finite, as in one dimensional Luttinger liquids. These fixed points can be either stable (attractive), when the disorder is associated to topological defects in the lattice or to a random mass term, or unstable (repulsive) when the disorder is induced by impurities outside the graphene planes. In addition, we analyze mid-gap states which can arise near interfaces or vacancies.Comment: 4 pages, 3 figure

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model and a non-integrable extended Hubbard model, and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.Comment: 13 pages, 4 pages appendix, 8 figure

First Order Superfluid to Bose Metal Transition in Systems with Resonant Pairing

Systems showing resonant superfluidity, driven by an exchange coupling of strength $g$ between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first order phase transition as $g$ increases beyond some critical value $g_c$. The superfluid phase for $g \leq g_c$ is characterized by a gap in the fermionic single particle spectrum and an acoustic sound-wave like collective mode of the bosonic resonating fermion pairs inside this gap. For $g>g_c$ this state gives way to a phase uncorrelated bosonic liquid with a $q^2$ spectrum.Comment: 5 pages, 3 figure

Entanglement at the boundary of spin chains near a quantum critical point and in systems with boundary critical points

We analyze the entanglement properties of spins (qubits) attached to the boundary of spin chains near quantum critical points, or to dissipative environments, near a boundary critical point, such as Kondo-like systems or the dissipative two level system. In the first case, we show that the properties of the entanglement are significantly different from those for bulk spins. The influence of the proximity to a transition is less marked at the boundary. In the second case, our results indicate that the entanglement changes abruptly at the point where coherent quantum oscillations cease to exist. The phase transition modifies significantly less the entanglement.Comment: 5 pages, 4 figure

Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

Universal asymptotic behavior in flow equations of dissipative systems

Based on two dissipative models, universal asymptotic behavior of flow equations for Hamiltonians is found and discussed. Universal asymptotic behavior only depends on fundamental bath properties but not on initial system parameters, and the integro-differential equations possess an universal attractor. The asymptotic flow of the Hamiltonian can be characterized by a non-local differential equation which only depends on one parameter - independent of the dissipative system or truncation scheme. Since the fixed point Hamiltonian is trivial, the physical information is completely transferred to the transformation of the observables. This yields a more stable flow which is crucial for the numerical evaluation of correlation functions. Furthermore, the low energy behavior of correlation functions is determined analytically. The presented procedure can also be applied if relevant perturbations are present as is demonstrated by evaluating dynamical correlation functions for sub-Ohmic environments. It can further be generalized to other dissipative systems.Comment: 15 pages, 9 figures; to appear in Phys. Rev.

Electron-electron interaction and charging effects in graphene quantum dots

We analyze charging effects in graphene quantum dots. Using a simple model, we show that, when the Fermi level is far from the neutrality point, charging effects lead to a shift in the electrostatic potential and the dot shows standard Coulomb blockade features. Near the neutrality point, surface states are partially occupied and the Coulomb interaction leads to a strongly correlated ground state which can be approximated by either a Wigner crystal or a Laughlin like wave function. The existence of strong correlations modify the transport properties which show non equilibrium effects, similar to those predicted for tunneling into other strongly correlated systems.Comment: Extended version accepted for publication at Phys. Rev.