arXiv subjects

Matthias Reitner

Publications and source records attributed to Matthias Reitner.

10 recordsLinked to original sources

arXiv2026

On Degeneracies of Density, Magnetic, and Pairing Responses: How Competing Orders Echo Underlying Symmetries in the Hubbard Model

Strongly correlated electron systems often display competing or even intertwined ordering tendencies, hinting to extremely close or degenerate many-electron energies. While degeneracies are directly rooted in the underlying symmetries of the problem under investigation, their multifaceted effects on different response functions and their mutual relations often remain elusive. Here we put this subject on a rigorous basis by investigating the degeneracies of charge, spin, and pairing susceptibilities for the unfrustrated, bipartite Hubbard model. Exploiting its pseudospin symmetry, we analytically derive the mutual relations between these response functions for generic spatial modulations, highly relevant, e.g., for the competition of stripe and superconducting orders. By means of two-particle numerical simulations we demonstrate the occurrence of a simultaneous $d$-wave pairing/$d$-density wave (loop current) instability in the vicinity of the metal-insulator transition, driven by short-ranged spin fluctuations for the two-dimensional case. We show how this degeneracy is gradually lifted by geometrical frustration, which favors superconductivity. Our study provides a general tool for revealing symmetry relations in correlated electron systems and establishes a unifying perspective on the nature of their intermingled charge/loop current, pairing, and spin orders.

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arXiv2025

Non-perturbative effects of short-range spatial correlations at the two-particle level

By means of cellular dynamical mean-field theory (CDMFT) we study how short-range correlations drive the breakdown of the self-consistent perturbation theory in two-dimensional systems and the most relevant physical consequences associated to it. To this aim, we first derive in a structured and consistent way the Bethe-Salpeter equation (BSE) formalism at the CDMFT level in all physical channels, explicitly addressing the important aspect of the related Ward identities. In this context, we perform systematic calculations of the BSE for the two-dimensional Hubbard model at half-filling at intermediate coupling. Our study illustrates how the divergence of a fundamental building block of the BSE in the charge channel, the two-particle irreducible vertex, systematically occurs at lower interactions than in the (purely local) DMFT case, due to short-range antiferromagnetic fluctuations. Further, the change of sign of the eigenvalues of the generalized charge susceptibility associated to the vertex divergences is identified as the essential prerequisite to drive, at larger interaction values, the physics of the Mott transition in two dimensions, as well as of the adjacent phase-separation instabilities.

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arXiv2025

Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations

We present a dynamical mean-field study of the nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.

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arXiv2025

Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications

Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise relation between two distinct issues previously considered equivalent: the misleading convergence in self-consistent schemes and the multivaluedness of the Luttinger-Ward functional. Although these problems are fundamentally linked through the divergences of the irreducible vertex function, we show that misleading convergence can occur even in the absence of such divergences. Eventually, a systematic procedure for stabilizing the physical solution is proposed.

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arXiv2024

Non-Perturbative Feats in the Physics of Correlated Antiferromagnets

In the last decades multifaceted manifestations of the breakdown of the self-consistent perturbation theory have been identified for the many-electron problem. Yet, the investigations have been so far mostly limited to paramagnetic states, where symmetry breaking is not allowed. Here, we extend the analysis to the spontaneously symmetry-broken antiferromagnetic (AF) phase of the repulsive Hubbard model. To this aim, we calculated two-particle quantities using dynamical mean-field theory for the AF-ordered Hubbard model and studied the possible occurrence of divergences of the irreducible vertex functions in the charge and spin sectors. Our calculations pinpoint the divergences in the AF phase diagram, showing that while the onset of AF order mitigates the breakdown of the perturbation expansion, it does not fully prevent it. Moreover, we have been able to link the changes in the dynamical structure of the corresponding generalized susceptibilities to the physical crossover from a weak-coupling (Slater) to a strong-coupling (Heisenberg) antiferromagnet, which takes place as the interaction strength is gradually increased. Finally, we discuss possible physical consequences of the irreducible vertex divergences in triggering phase-separation instabilities within the AF phase and elaborate on the implications of our findings for two-dimensional systems, where the onset of a long-range AF order is prevented by the Mermin-Wagner theorem.

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arXiv2024

General Shiba mapping for on-site four-point correlation functions

By applying the Shiba mapping on the two particle level, we derive the relation between the local four-point correlation functions of bipartite lattice models with on-site electronic repulsion and those of the corresponding models with attractive interaction in the most general setting. In particular, we extend the results of [Phys. Rev. B, 101, 155148 (2020)], which were limited to the rather specific situation of the static limit in strictly particle-hole symmetric models, (i) by explicitly including both magnetic field and different values of the chemical potentials, and (ii) by considering the full dependence of the generalized susceptibilities on the transfer (bosonic) Matsubara frequency. The derived formalism is then applied, as a relevant benchmark, to the Hubbard atom, by investigating the general properties of the divergences of its irreducible vertex functions as a function of chemical potential and applied magnetic field. The resulting phase-diagrams provide an insightful compass for future studies of the breakdown of the self-consistent perturbation expansion beyond high-symmetric regimes.

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arXiv2023

Fermi and Luttinger arcs: two concepts, realized on one surface

We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable to drive the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs") as well as of the opening of a pseudogap at hole- and electron-doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc.

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arXiv2023

Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities

At thermal equilibrium, we find that generalized susceptibilities encoding the static physical response properties of Hermitian many-electron systems possess inherent non-Hermitian (NH) matrix symmetries. This leads to the generic occurrence of exceptional points (EPs), i.e., NH spectral degeneracies, in the generalized susceptibilities of prototypical Fermi-Hubbard models, as a function of a single parameter such as chemical potential. We demonstrate that these EPs are necessary to promote correlation-induced thermodynamic instabilities, such as phase-separation occurring in the proximity of a Mott transition, to a topologically stable phenomenon.

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arXiv2023

Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region

We thoroughly analyze the divergences of the irreducible vertex functions occurring in the charge channel of the half-filled Hubbard model in close proximity to the Mott metal-insulator transition (MIT). In particular, by systematically performing dynamical mean-field theory (DMFT) calculations on the two-particle level, we determine the location and the number of the vertex divergences across the whole coexistence region adjacent to the first-order metal-to-insulator transition. We find that the lines in the parameter space, along which the vertex divergences occur, display a qualitatively different shape in the coexisting metallic and insulating phase, which is also associated to an abrupt jump of the number of divergences across the MIT. Physically, the systematically larger number of divergences on the insulating side of the transition reflects the sudden suppression of local charge fluctuation at the MIT. Further, a systematic analysis of the results demonstrates that the number of divergence lines increases as a function of the inverse temperature ${\beta\!=\!(k_\mathrm{B} T)^{-1}}$ by approaching the Mott transition in the zero temperature limit. This makes it possible to identify the zero-temperature MIT as an accumulation point of an infinite number of vertex divergence lines, unveiling the highly nonperturbative nature of the underlying transition.

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arXiv2020

Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems

We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches in correlated regimes.

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