arXiv subjects

Aiman Al-Eryani

Publications and source records attributed to Aiman Al-Eryani.

10 recordsLinked to original sources

arXiv2026

Structural symmetry effects on the competition of density waves and superconductivity in bilayer nickelates

We investigate the interplay between spin-density-wave (SDW) order and superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ using the functional renormalization group~(fRG) applied to multiorbital weak-coupling models of both the ambient- and high-pressure crystal structures. As Hund's coupling increases, the leading instability evolves from superconductivity to an SDW state with ordering vector $\mathbf{Q}_1 \approx (π/2,π/2)$ (equivalently $\mathbf{Q}_Y \approx (0,π)$ in the orthorhombic $Amam$ unit cell), in agreement with experimental observations. Surprisingly, the ambient- and high-pressure structures exhibit nearly identical non-interacting susceptibilities and leading fRG instabilities, indicating that the emergence of superconductivity under pressure cannot be explained solely by changes in the low-energy electronic structure. Instead, our results identify the suppression of orthorhombicity as a key ingredient for superconductivity. As the system approaches the tetragonal limit, symmetry-related SDW fluctuations become nearly degenerate, frustrating long-range magnetic order while enhancing pairing interactions. These findings highlight lattice symmetry as a central tuning parameter of the competing ordered states in bilayer nickelates and suggest that reducing orthorhombicity through uniaxial strain could stabilize bulk superconductivity already at ambient pressure.

cond-mat.supr-con↗

arXiv2026

Multiloop functional renormalization group from single bosons

The functional renormalization group (fRG) is an established tool in the treatment of correlated electron systems, notably for the description of competing instabilities. In recent years, methodological advancements led to the multiloop extension of the fRG, which systematically includes loop corrections beyond the conventional one-loop truncation and yields a quantitatively accurate description of two-dimensional lattice systems. At the same time, the single-boson exchange (SBE) decomposition of the two-particle vertex has been shown to offer both computational and interpretative advantages paving the way to more affordable approximation schemes. We here apply their combination coined as multiloop SBE fRG to the two-dimensional Hubbard model at weak coupling. After providing a detailed account of the underlying formalism in physical channels, we analyze the results for the frequency- and momentum-dependent vertex functions. We find that the SBE approximation, i.e., neglecting the flow of the multi-boson exchange contributions, accurately reproduces the parquet approximation at loop convergence. The presented algorithmic improvement opens the route for the treatment of more challenging parameter regimes and more realistic models.

cond-mat.str-el↗

arXiv2026

Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems

The functional renormalization group (fRG) is acknowledged as a powerful tool in quantum many-body physics and beyond. On the technical side, conventional implementations of the fRG rely on regulators for bare propagators only. Starting from Schwinger--Dyson and Bethe--Salpeter equations, we develop here an fRG formulation where both bare propagators and bare interactions can be dressed with regulators. The approach thus obtained is an extension of the multiloop fRG recently introduced for many-fermion systems. Using the single-boson exchange decomposition, we show that the underlying flow equations are simply interpreted as adding a regulator to the bosonic propagator and that such an extension scarcely changes the original structure of the flow equations. Overall, we provide a framework for implementing approaches that cannot be realized with conventional fRG methods, such as temperature flows for models with retarded interactions. For concrete applications, we analyze the loop convergence of our scheme against conventional cutoff schemes for the Anderson impurity model. Finally, we devise a new temperature-flow scheme that implements a cutoff in both the propagator and the bare interaction, and demonstrate its validity on a model of an Anderson impurity coupled to a phonon.

cond-mat.str-el↗

arXiv2026

BosonFlow: A C++ codebase for dynamic fRG and single-boson exchange in correlated fermion systems

We present a unified C++ implementation of the functional renormalization group and the parquet equations within the single-boson exchange formalism for several paradigmatic tight-binding and impurity models at equilibrium. The implementation computes the full dynamic vertex and self-energies, with momentum dependence treated using a truncated unity framework. We implement multiple self-energy flow equations, cutoff schemes, and extensions ranging from the dynamical functional renormalization group to multiloop flow equations that incorporate cutoffs in both the propagator and the interaction. The codebase serves as a reference for recent developments in the fRG and parquet methods for correlated electron systems and provides a flexible foundation for developing new many-body approaches and extensions.

cond-mat.str-el↗

arXiv2026

Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization

Electron-electron and electron-phonon interactions are responsible for the formation of spin, charge, and superconducting correlations in layered quantum materials. A paradigmatic model for such materials that captures both kinds of interactions is the two-dimensional Hubbard-Holstein model with a dispersionless Einstein phonon. In this work, we provide a detailed analysis of the magnetic, density, and superconducting fluctuations at and away from half-filling. To that end, we employ the functional renormalization group using the recently introduced extension of the single-boson exchange formulation. More precisely, we go beyond previous approaches to the model by resolving the full frequency dependence of the two-particle vertex and taking into account the feedback from the electronic self-energy. We perform broad parameter scans in the space of Hubbard repulsion, electron-phonon coupling strength, and phonon frequency to explore the leading magnetic, density, and superconducting susceptibilities from the adiabatic to the anti-adiabatic regime. Our numerical data reveal that self-energy effects lead to an enhancement of the $d$-wave superconducting susceptibility towards larger phonon frequencies, in contrast to earlier isotope-effect studies. At small phonon frequencies, large density contributions to the $s$-wave superconducting susceptibility change sign and eventually lead to a reduction of $s$-wave superconductivity with increasing electron-phonon coupling, signaling the breakdown of Migdal-Eliashberg theory. We analyze our findings systematically, employing detailed diagnostics of the intertwined fluctuations and pinning down the various positive and negative isotope effects of the physical susceptibilities.

cond-mat.str-el↗

arXiv2026

Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches

The parquet equations present a cornerstone of some of the most important diagrammatic many-body approximations and methods currently on the market for strongly correlated materials: from non-local extensions of the dynamical mean-field theory to the functional renormalization group. The recently introduced single-boson exchange decomposition of the vertex presents an alternative set of equivalent equations in terms of screened interactions, Hedin vertices, and rest functions. This formulation has garnered much attention for several reasons: opening the door to new approximations, for avoiding vertex divergences associated with local moment formation plaguing the traditional parquet decomposition, and for its interpretative advantage in its built-in diagrammatic identification of bosons without resorting to Hubbard-Stratonovich transformations. In this work, we show how the fermionic diagrams of the particle-particle and particle-hole polarizations in the SBE formalism can be mapped to diagrammatics of a bosonic self-energy of two respective bosonic theories with pure bosonic constituents, solidifying the identification of the screened interaction with a bosonic propagator. Resorting to a spin-diagonalized basis for the bosonic fields and neglecting the coupling between singlet and triplet components is shown to recover the trace log theory known from Hubbard-Stratonovich transformations. Armed with this concrete mapping, we revisit a conjecture claiming that universal aspects of the parquet approximation coincide with those of a self-consistent large-$N$ approximation for a bosonic $O(N)$ model. We comment on the role of the self-energy and crossing symmetry in enforcing the Hohenberg-Mermin-Wagner theorem in parquet-related approaches.

cond-mat.str-el↗

arXiv2026

Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group

We extend the recently introduced single-boson exchange formulation to the computation of the self-energy from the Schwinger--Dyson equation (SDE). In particular, we derive its expression both in diagrammatic and in physical channels. The simple form of the single-boson exchange SDE, involving only the bosonic propagator and the fermion-boson vertex, but not the rest function, allows for an efficient numerical implementation. We furthermore discuss its implications in a truncated unity solver, where a restricted number of form factors introduces an information loss in the projection of the momentum dependence that in general affects the equivalence between the different channel representations. In the application to the functional renormalization group, we find that the convergence in the number of form factors depends on the channel representation of the SDE. For the two-dimensional Hubbard model at weak coupling, the pseudogap opening driven by antiferromagnetic fluctuations is captured already by a single ($s$-wave) form factor in the magnetic channel representation, differently to the density and superconducting channels.

cond-mat.str-el↗

arXiv2025

Relativistic Mott transition and high-order van Hove singularity in twisted double bilayer WSe${}_2$: mean-field and functional renormalization group study

Experiments on twisted double bilayer tungsten diselenide have demonstrated that moir'e semiconductors can realize a relativistic Mott transition, i.e., a quantum phase transition from a Dirac semimetal to a correlated insulating state, by twist-angle tuning. In addition, signatures of van Hove singularities were observed in the material's moir'e valence bands, suggesting further potential for the emergence of strongly-correlated states. Based on a continuum model, we provide a detailed analysis of the twist-angle dependence of the system's band structure, focusing on the evolution of the Dirac excitations and the Fermi-surface structure with its Lifshitz transitions across the van Hove fillings. We exhibit that the twist angle can be used to band engineer a high-order van Hove singularity, which can be accessed by gate tuning. We then study the magnetic phase diagram of an effective Hubbard model for twisted double bilayer tungsten diselenide on the effective honeycomb superlattice with tight-binding parameters fitted to the two topmost bands of the continuum model. To that end, we employ a self-consistent Hartree-Fock mean-field approach in real space. Fixing the angle-dependent Hubbard interaction based on the experimental findings, we explore a broad parameter range of twist angle, filling, and temperature. We find a rich variety of magnetic states that we expect to be accessible in future experiments, including, e.g., a non-coplanar spin-density wave with non-zero spin chirality and a half-metallic uniaxial spin-density wave. Finally, we employ a functional renormalization group approach to also study the competition between density-wave and superconducting instabilities. For twist angles of $θ=2.0^\circ, 2.5^\circ$, as well as $θ\approx 3.5^\circ$ -- where the high-order van Hove-singularity is found -- we find clear indications for unconventional superconductivity.

cond-mat.mes-hall↗

arXiv2024

Screening and effective RPA-like charge susceptibility in the extended Hubbard model

We generalize the recently introduced single-boson exchange formalism to nonlocal interactions. In the functional renormalization group application to the extended Hubbard model in two dimensions, we show that the flow of the rest function can be neglected up to moderate interaction strengths. We explore the physics arising from the interplay between onsite and nearest-neighbor interactions in various parameter regimes by performing a fluctuation diagnostics. Differently from the magnetic and superconducting susceptibilities, the charge susceptibility appears to be described by the random phase approximation (RPA). We show that this behavior can be traced back to cancellations in the renormalization of the density fermion-boson coupling.

cond-mat.str-el↗

arXiv2023

Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling

We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.

cond-mat.str-el↗