Non-Fermi-liquid behaviour and Fermi-surface expansion induced by van Hove-driven ferromagnetic fluctuations: the D-TRILEX analysis

TL;DR

The paper addresses non-Fermi-liquid behavior near a van Hove singularity in a 2D Hubbard model with ferromagnetic fluctuations by applying the D-TRILEX method to include non-local self-energies and three-point vertex corrections. It demonstrates that non-local fluctuations strongly damp quasiparticles and induce a momentum-differentiated spectral response, including a splitting of the spectral function near the Fermi level while the Fermi surface itself expands due to spectral-weight redistribution. Self-consistent treatment of non-local quantities and proper vertex corrections prove essential to capture these effects, revealing limitations of purely local DMFT and some D$\\Gamma$A variants. The findings underscore the role of van Hove topology in stabilizing NFL behavior and suggest avenues for extending the framework to multi-orbital systems and more realistic materials via DFT+DMFT integrations.

Abstract

We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings $t'/t=-0.45$, which favours the ferromagnetic instability. We find, that a self-consistent consideration of the ferromagnetic fluctuations within the D-TRILEX approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit, but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the non-local contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behaviour.

Figures (7)

• Figure 1: Phase diagram in the $n$–$T$ plane obtained within fRG (green line), DMFT (blue line), and D-TRILEX (red points). The $(Q,Q)$ region indicates an incommensurate magnetic phase, while FM denotes the ferromagnetic one.
• Figure 2: Self-Energies on Matsubara frequencies at $n = 0.43$ (a-d) and $n=0.52$ (e-h). (a,e) DMFT, (b,f) D-TRILEX X-point, (c,g) D-TRILEX nodal point, (d,h) D-TRILEX anti-nodal point. The data have been extrapolated to zero frequency by a polynomial fit.
• Figure 3: Quasiparticle damping $\gamma = -\mathrm{Im}\Sigma_{{\mathbf k},\nu = 0}$ in D-TRILEX at ${\mathbf k}=X=(\pi,0)$ (dashed lines) and DMFT (solid lines) as functions of temperature for $n = 0.43$, $0.46$ and $0.53$
• Figure 4: Momentum-resolved spectral functions for $T = 0.05$, $n = 0.43$. Panels (a–f): (a) D-TRILEX; (b) DMFT; (c) D$\Gamma$A with $\lambda$-correction; (d) D-TRILEX single-shot; (e) D$\Gamma$A without $\lambda$ correction; (f) self-consistent D$\Gamma$A.
• Figure 5: Spectral functions in D-TRILEX at $n = 0.43$ at the X point (red line), nodal and antinodal points (green and blue lines) (a) $T = 0.1$, (b) $T = 0.05$