arXiv subjects

Herbert Eßl

Publications and source records attributed to Herbert Eßl.

6 recordsLinked to original sources

arXiv2026

Non-Perturbative Resolution of Luttinger's Theorem Violations in Strongly Correlated Systems

Many-body physics faces an apparent paradox concerning violations of Luttinger's theorem in strongly correlated systems. The theorem relates the electron number to the Luttinger count -- the monodromy of the logarithm of the imaginary-frequency Green's function $G(iε)$ -- and, at finite magnetic field, connects the Hall conductivity to the magnetic-field derivative of the Luttinger count via the Streda formula. Here, we provide a non-perturbative solution to this paradox. We demonstrate that the reported violations of Luttinger's theorem do not require a breakdown of the skeleton diagram representation of physical quantities, thereby resolving a long-standing point of contention in many-body theory. Furthermore, we show that the Luttinger integral, which accounts for the mismatch between the particle number and the Luttinger count, is itself a genuine topological invariant directly tied to the Luttinger-Ward functional $Φ[G]$ rather than to the Green's function alone. We demonstrate that this invariant, like the monodromy of $\ln G(iε)$ itself, stems exclusively from the zero-frequency discontinuity of the Matsubara trajectory.

cond-mat.str-el↗

arXiv2026

Stabilizing the parquet problem

We systematically analyze the stability of the iterative solution of the parquet equations by studying the spectrum of the Jacobian associated with the commonly used damped fixed-point iteration procedure. In this context, we provide an explicit criterion that determines when the physical fixed point of the parquet iteration becomes unstable. Importantly, we demonstrate that misleading convergence issues, observed in parquet calculations at intermediate-to-high interaction values, are not restricted to parameter regions where the two-particle irreducible vertex diverges, but can also arise in absence of vertex divergences. Hence, the misleading convergence issues of parquet-based algorithms are not directly caused by the crossings of two solutions of the (multivalued) Luttinger-Ward functional, that are associated with vertex divergences. Building on these insights, we apply the controlled stabilization strategy of Phys. Rev. Lett. 137, 016502 (2026) to the challenging case of the parquet iteration. This strategy allows the convergence to the physical solution in the instability regimes. We apply this procedure to the zero-point model and the Hubbard model in the atomic limit, where we successfully stabilize the physical solution deep in the non-perturbative regime, even across multiple divergence lines. Further, we compare our stabilization strategy to alternative fixed-point solvers that can be used to solve the parquet problem.

cond-mat.str-el↗

arXiv2026

Instabilities in self-consistent diagrammatic approaches and how to cure them

While self-consistent diagrammatic approaches are widely used to compute the physical properties of correlated quantum materials, their applicability may get severely hindered precisely in the parameter regions where the most exciting physics is observed. One of the major issues, referred to as "misleading convergence", is the tendency of iterative schemes to converge to unphysical fixed points for intermediate-to-strong electronic interactions, regardless of the numerical accuracy of the computation. Here, we explicitly verify that the origin of this problem in several established self-consistent many-electron approaches, defined in the general diagrammatic framework of the boson-exchange formalism, resides exclusively in the stability condition of the respective iteration schemes, and not in an intrinsic breakdown of their self-consistent diagrammatic description. This insight enables a simple and general remedy, as recently proposed in Phys. Rev. Lett. 137, 016502 (2026): The redefinition of the iterative procedure, by inverting the unstable eigendirections of the Jacobian associated with the fixed point of the self-consistent algorithm. We illustrate the successful outcome of this procedure by means of systematic calculations performed on exactly solvable testbed models. Our results demonstrate that the physical fixed point of the diagrammatic schemes we considered can be stabilized, de facto, across the entire parameter range, including the most challenging nonperturbative/strong-coupling regimes.

cond-mat.str-el↗

arXiv2026

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗