Stability of the Néel quantum critical point in the presence of Dirac fermions

• Published in: arXiv.org
• Main Authors: Hu, Huanzhi, Lin, Jennifer, Uryszek, Mikolaj D, Krüger, Frank
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.02.2023
• Subjects: Antiferromagnetism; Broken symmetry; Conduction electrons; Coupling; Critical point; Electron spin; Elementary excitations; Fermions; Field theory; Flavor (particle physics); Landau damping; Order parameters; Physics - Strongly Correlated Electrons; Stability
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2210.06577

We investigate the stability of the Néel quantum critical point of two-dimensional quantum antiferromagnets, described by a non-linear \(\sigma\) model (NL\(\sigma\)M), in the presence of a Kondo coupling to \(N_f\) flavours of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using momentum-shell RG, we demonstrate that the Landau damping is weakly irrelevant at the Néel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the Néel quantum critical point quasi-stable for \(N_f\ge 4\) and thermodynamically stable for \(N_f<4\). In the latter case, we identify a new multi-critical point which describes the transition between the Néel critical and Kondo run-away regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multi-critical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.