Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures

Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One such recently proposed numerical technique are neural quantum states. This new type of wave-function-based Ansatz utilizes the expressivity of neural networks to tackle fundamentally challenging problems, such as the Mott transition. In this paper, we aim to gauge the universalness of one representative of neural network Ansätze, the hidden-fermion slater determinant approach. To this end, we study five different fermionic models each displaying volume law scaling of the entanglement entropy. For these, we correlate the effectiveness of the Ansatz with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional Ansatz becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliably, the neural network approach also works reliably and efficiently. This highlights the great potential of neural network approaches, but also the inherent challenges: finding suitable points in theory space around which to construct the Ansatz in order to be able to efficiently treat models unsuitable for their current designs

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

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

divERGe implements various Exact Renormalization Group examples

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU$^2$FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.Comment: 42 pages, 7 figures, git repo at https://git.rwth-aachen.de/frg/diverge.gi

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

Spin and charge fluctuation induced pairing in ABCB tetralayer graphene

Motivated by the recent experimental realization of ABCB stacked tetralayer graphene [Wirth et al., ACS Nano 16, 16617 (2022)], we study correlated phenomena in moiré-less graphene tetralayers for realistic interaction profiles using an orbital resolved random phase approximation approach. We demonstrate that magnetic fluctuations originating from local interactions are crucial close to the van Hove singularities on the electron- and hole-doped side promoting layer selective ferrimagnetic states. Spin fluctuations around these magnetic states enhance unconventional spin-triplet, valley-singlet superconductivity with f-wave symmetry due to intervalley scattering. Charge fluctuations arising from long range Coulomb interactions promote doubly degenerate p-wave superconductivity close to the van Hove singularities. At the conduction band edge of ABCB graphene, we find that both spin and charge fluctuations drive f-wave superconductivity. Our analysis suggests a strong competition between superconducting states emerging from long- and short-ranged Coulomb interactions and thus stresses the importance of microscopically derived interaction profiles to make reliable predictions for the origin of superconductivity in graphene-based heterostructures

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

Magic angle of Sr2RuO4 : optimizing correlation-driven superconductivity

Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr2RuO4 to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting Tc and a dominant dx2-y2 pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.Peer reviewe

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