TU2^2FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models

Describing the emergence of phases of condensed matter is one of the central challenges in physics. For this purpose many numerical and analytical methods have been developed, each with their own strengths and limitations. The functional renormalization group is one of these methods bridging between efficiency and accuracy. In this paper we derive a new truncated unity (TU) approach unifying real- and momentum space TU, called TU$^2$FRG. This formalism significantly improves the scaling compared to conventional momentum (TU)FRG when applied to large unit-cell models and models where the translational symmetry is broken.Comment: 9 pages, 4 figure

Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases

The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there is a lack in the theoretical literature concerning the systematic study of the effects of the trap potential as well as the finite size of the systems, as numerical studies of such non periodic, correlated fermionic lattices models are numerically demanding beyond one dimension. We use the recently introduced real-space truncated unity functional renormalization group to study these boundary and trap effects with a focus on their impact on the superconducting phase of the $2$D Hubbard model. We find that in the experiments not only lower temperatures need to be reached compared to current capabilities, but also system size and trap potential shape play a crucial role to simulate emergent phases of matter.Comment: 21 pages, 9 Figure

Superconductivity of repulsive spinless fermions with sublattice potentials

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered $d$-wave and $f$-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the square lattice displays a much richer phase diagram including topological $p+ip$ superconductivity which is induced by a qualitatively different mechanism compared to the $d$-wave pairing. We illuminate this from several complementary perspectives: We analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive functional renormalization group and and density matrix renormalization group calculations.Comment: 6+6 page

Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study

The Rashba-Hubbard model on the square lattice is the paradigmatic case for studying the effect of spin-orbit coupling, which breaks spin and inversion symmetry, in a correlated electron system. We employ a truncated-unity variant of the functional renormalization group which allows us to analyze magnetic and superconducting instabilities on equal footing. We derive phase diagrams depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor hopping and electron filling. We find commensurate and incommensurate magnetic phases which compete with d-wave superconductivity. Due to the breaking of inversion symmetry, singlet and triplet components mix; we quantify the mixing of d-wave singlet pairing with f-wave triplet pairing.Comment: 9 pages, 7 figure

Experimental Observation of ABCB Stacked Tetralayer Graphene

In tetralayer graphene, three inequivalent layer stackings should exist; however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the elusive third stacking (ABCB) being unique as it is predicted to exhibit an intrinsic bandgap as well as locally flat bands around the K points. Here, we use scattering-type scanning near-field optical microscopy and confocal Raman microscopy to identify and characterize domains of ABCB stacked tetralayer graphene. We differentiate between the three stacking sequences by addressing characteristic interband contributions in the optical conductivity between 0.28 and 0.56 eV with amplitude and phase-resolved near-field nanospectroscopy. By normalizing adjacent flakes to each other, we achieve good agreement between theory and experiment, allowing for the unambiguous assignment of ABCB domains in tetralayer graphene. These results establish near-field spectroscopy at the interband transitions as a semiquantitative tool, enabling the recognition of ABCB domains in tetralayer graphene flakes and, therefore, providing a basis to study correlation physics of this exciting phase

Abatement of styrene waste gas emission by biofilter and biotrickling filter: comparison of packing materials and inoculation procedures

The removal of styrene was studied using 2 biofilters packed with peat and coconut fibre (BF1-P and BF2-C, respectively) and 1 biotrickling filter (BTF) packed with plastic rings. Two inoculation procedures were applied: an enriched culture with strain Pseudomonas putida CECT 324 for biofilters and activated sludge from a municipal wastewater treatment plant for the BTF. Inlet loads (ILs) between 10 and 45 g m-3 h-1 and empty bed residence times (EBRTs) from 30 to 120 s were applied. At inlet concentrations ranging between 200 and 400 mg Nm-3, removal efficiencies between 70 and 95% were obtained in the 3 bioreactors. Maximum elimination capacities (ECs) of 81 and 39 g m-3 h-1 were obtained for the first quarter of the BF1-P and BF2-C, respectively (IL of 173 g m-3 h-1 and EBRT of 60 s in BF1-P; IL of 89 g m-3 h-1 and EBRT of 90 s in BF2-C). A maximum EC of 52 g m-3 h-1 was obtained for the first third of the BTF (IL of 116 g m-3 h-1, EBRT of 45 s). Problems regarding high pressure drop appeared in the peat biofilter, whereas drying episodes occurred in the coconut fibre biofilter. DGGE revealed that the pure culture used for biofilter inoculation was not detected by day 105. Although 2 different inoculation procedures were applied, similar styrene removal at the end of the experiments was observed. The use as inoculum of activated sludge from municipal wastewater treatment plant appears a more feasible option

Cerebral palsy in a total population of 4–11 year olds in southern Sweden. Prevalence and distribution according to different CP classification systems

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to investigate the prevalence of cerebral palsy (CP) as well as to characterize the CP population, its participation in a secondary prevention programme (CPUP) and to validate the CPUP database.</p> <p>Methods</p> <p>The study population was born 1990–1997 and resident in Skåne/Blekinge on Jan 1^st2002. Multiple sources were used. Irrespective of earlier diagnoses, neuropaediatrician and other professional medical records were evaluated for all children at the child habilitation units. The CPUP database and diagnosis registers at hospital departments were searched for children with CP or psychomotor retardation, whose records were then evaluated. To enhance early prevention, CP/probable CP was searched for also in children below four years of age born 1998–2001.</p> <p>Results</p> <p>The prevalence of CP was 2.4/1,000 (95% CI 2.1–2.6) in children 4–11 years of age born in Sweden, excluding post-neonatally acquired CP. Children born abroad had a higher prevalence of CP with more severe functional limitations. In the total population, the prevalence of CP was 2.7/1,000 (95% CI 2.4–3.0) and 48% were GMFCS-level I (the mildest limitation of gross motor function).</p> <p>One third of the children with CP, who were born or had moved into the area after a previous study in 1998, were not in the CPUP database. The subtype classification in the CPUP database was adjusted in the case of every fifth child aged 4–7 years not previously reviewed.</p> <p>Conclusion</p> <p>The prevalence of CP and the subtype distribution did not differ from that reported in other studies, although the proportion of mild CP tended to be higher.</p> <p>The availability of a second opinion about the classification of CP/CP subtypes is necessary in order to keep a CP register valid, as well as an active search for undiagnosed CP among children with other impairments.</p

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects