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Renormalization group study of the Hubbard model at the van Hove singular point

Nobuo Furukawa, Carsten Honerkamp A, Manfred Salmhofer B +1 more

Physica B Condensed MatterJul 1, 20003 citations

Fermi Liquid Properties of a Two Dimensional Electron Liquid Near Van-Hove Singularities

David Menashe, Boris Laikhtman

APSMar 1, 19980 citations

The Role of the Van Hove Singularity in the Quantum Criticality of the Hubbard Model

Sandeep Pathak, K. S. Chen, Shuxiang Yang +2 more

APSMar 1, 20110 citations

The van Hove Singularity and Two-Dimensional Superconductivity. Exact Analytical Results

Radosław Szczȩśniak, S. Grabiński

Acta Physica Polonica ASep 1, 200210 citations

Wilsonian effective field theory of two-dimensional Van Hove singularities

Anton Kapustin, Tristan McKinney, Ira Z. Rothstein

We study two-dimensional fermions with a short-range interaction in the presence of a Van Hove singularity. It is shown that this system can be consistently described by an effective field theory whose Fermi surface is subdivided into regions as defined by a factorization scale, and that the theory is renormalizable in the sense that all of the counterterms are well defined in the IR limit. The theory has the unusual feature that the renormalization-group equation for the coupling has an explicit dependence on the renormalization scale, much as in theories of Wilson lines. In contrast to the case of a round Fermi surface, there are multiple marginal interactions with nontrivial RG flow. The Cooper instability remains strongest in the BCS channel. We also show that the marginal Fermi-liquid scenario for the quasiparticle width is a robust consequence of the Van Hove singularity. Our results are universal in the sense that they do not depend on the detailed properties of the Fermi surface away from the singularity.We study two-dimensional fermions with a short-range interaction in the presence of a Van Hove singularity. It is shown that this system can be consistently described by an effective field theory whose Fermi surface is subdivided into regions as defined by a factorization scale, and that the theory is renormalizable in the sense that all of the counterterms are well defined in the IR limit. The theory has the unusual feature that the renormalization-group equation for the coupling has an explicit dependence on the renormalization scale, much as in theories of Wilson lines. In contrast to the case of a round Fermi surface, there are multiple marginal interactions with nontrivial RG flow. The Cooper instability remains strongest in the BCS channel. We also show that the marginal Fermi-liquid scenario for the quasiparticle width is a robust consequence of the Van Hove singularity. Our results are universal in the sense that they do not depend on the detailed properties of the Fermi surface away from the singularity.

arXiv:1601.03150Physical review. B./Physical review. BJul 17, 20187 citations

Ferromagnetic instability in itinerant fcc lattice electron systems with higher-order van Hove singularities: Functional renormalization group study

P. A. Igoshev, A. A. Katanin

We investigate the possibility of ferromagnetic ordering in the nondegenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher-order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The chemical potential versus temperature phase diagrams are calculated. We find ferromagnetic order only for sufficiently strong divergence of the density of states and fillings in the vicinity of van Hove singularity. The obtained Curie temperature is more than an order of magnitude smaller than the results of the random-phase approximation. The main origin of the suppression of ferromagnetism is the screening of interaction in the particle-particle channel. We also do not find the pronounced tendency towards incommensurate order when the Fermi level is moved away from a van Hove singularity, such that the first-order quantum phase transitions from the ferro- to paramagnetic phase are obtained.We investigate the possibility of ferromagnetic ordering in the nondegenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher-order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The chemical potential versus temperature phase diagrams are calculated. We find ferromagnetic order only for sufficiently strong divergence of the density of states and fillings in the vicinity of van Hove singularity. The obtained Curie temperature is more than an order of magnitude smaller than the results of the random-phase approximation. The main origin of the suppression of ferromagnetism is the screening of interaction in the particle-particle channel. We also do not find the pronounced tendency towards incommensurate order when the Fermi level is moved away from a van Hove singularity, such that the first-order quantum phase transitions from the ferro- to paramagnetic phase are obtained.

arXiv:2212.04135Physical review. B./Physical review. BMar 3, 20237 citations

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

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Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

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