Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9905166 · Physical Review Letters

Kinematics of Electrons near a Van Hove Singularity

J. González, F. Guinea, María A. H. Vozmediano

Published May 22, 2000• 40 citations
arXivHTMLPDF

Abstract

A two-dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of electron scattering in this model. The similarities and differences between a standard renormalization group approach and previous work based on parquet summations of log (2) divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.

DOI
10.1103/physrevlett.84.4930

Related papers

Effects of van Hove singularities on magnetism and superconductivity in the t − t ′ Hubbard model: A parquet approach

V. Yu. Irkhin, A. A. Katanin, Mikhail I. Katsnelson

The $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.

arXiv:cond-mat/0102381•Physical review. B, Condensed matter•Oct 3, 2001•96 citations

Fermi-liquid properties of a two-dimensional electron system with the Fermi level near a van Hove singularity

David Menashe, Boris Laikhtman

We use a diagrammatic approach to study low-energy physics of a two-dimensional electron system where the Fermi level is near van Hove singularities in the energy spectrum. We find that in most regions of the ${\ensuremath{\epsilon}}_{F}\ensuremath{-}T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self-energy is much smaller than the excitation energy, which implies well-defined quasiparticle excitations, and single-particle properties are only weakly affected by the presence of the van Hove singularities. The relevance to high-temperature superconductivity is also discussed.

arXiv:cond-mat/9905399•Physical review. B, Condensed matter•Jun 1, 1999•11 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.

arXiv:1601.03150•Physical review. B./Physical review. B•Jul 17, 2018•7 citations

Weakly interacting electrons and the renormalization group

Benedikt Binz, D. Baeriswyl, Benoît Douçot

We present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. As an example, we show the occurrence of d-wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one-loop) order on a most elementary level, connecting the idea of the “parquet summation” to the more modern concept of Wilson's effective action. The validity and restrictions of the one-loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two-dimensional Fermi system at Van Hove filling without nesting.

arXiv:cond-mat/0309645•Annalen der Physik•Nov 14, 2003•19 citations

The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities

Tristan McKinney

The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.

•Jun 12, 2018•0 citations

Charge instabilities near a Van Hove singularity

J. González

The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a Wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all scales, allowing a rigorous determination of spin and charge instabilities of the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model. Regarding the latter, repulsive interactions fall into two different universality classes. One of them has nonsingular response functions in the charge sector, while the other is characterized by the splitting of the Van Hove singularity. At the level of marginal perturbations, the Hubbard model turns out to be at the boundary between the two universality classes, while extended models with nearest-neighbor repulsive interactions belong to the latter class. In the case of open systems allowed to exchange particles with a reservoir, we show the existence of a range of fillings forbidden above and below the Van Hove singularity. This has the property of attracting the Fermi level in the mentioned range, as the system reaches its lowest energy when the Fermi energy is at the singularity.

arXiv:cond-mat/0007348•Physical review. B, Condensed matter•Jan 1, 2001•19 citations
A two-dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of electron scattering in this model. The similarities and differences between a standard renormalization group approach and previous work based on parquet summations of log (2) divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.
The $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.
We use a diagrammatic approach to study low-energy physics of a two-dimensional electron system where the Fermi level is near van Hove singularities in the energy spectrum. We find that in most regions of the ${\ensuremath{\epsilon}}_{F}\ensuremath{-}T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self-energy is much smaller than the excitation energy, which implies well-defined quasiparticle excitations, and single-particle properties are only weakly affected by the presence of the van Hove singularities. The relevance to high-temperature superconductivity is also discussed.
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 present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. As an example, we show the occurrence of d-wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one-loop) order on a most elementary level, connecting the idea of the “parquet summation” to the more modern concept of Wilson's effective action. The validity and restrictions of the one-loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two-dimensional Fermi system at Van Hove filling without nesting.
The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.
The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a Wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all scales, allowing a rigorous determination of spin and charge instabilities of the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model. Regarding the latter, repulsive interactions fall into two different universality classes. One of them has nonsingular response functions in the charge sector, while the other is characterized by the splitting of the Van Hove singularity. At the level of marginal perturbations, the Hubbard model turns out to be at the boundary between the two universality classes, while extended models with nearest-neighbor repulsive interactions belong to the latter class. In the case of open systems allowed to exchange particles with a reservoir, we show the existence of a range of fillings forbidden above and below the Van Hove singularity. This has the property of attracting the Fermi level in the mentioned range, as the system reaches its lowest energy when the Fermi energy is at the singularity.