Renormalization in Condensed Matter: Fermionic Systems - from Mathematics to Materials

Abstract

Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to applications in models relevant for materials science, such as the prediction of equilibrium phases of systems with competing ordering tendencies, and quantum criticality.

33 pages, 13 figures, to appear in the memorial volume dedicated to Wolfhart Zimmermann

References in corpus (9)

• Exact evolution equation for the effective potential
• "Deconfined" quantum critical points
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
• Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow
• Clustering of fermionic truncated expectation values via functional integration
• Singular Fermi Surfaces II. The Two--Dimensional Case
• Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases
• Low-Energy Effective Theory at a Quantum Critical Point of the Two-Dimensional Hubbard Model: Mean-Field Analysis

Cited by in corpus (10)

• The nonperturbative functional renormalization group and its applications
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Generalized local charge conservation in many-body quantum mechanics
• Tensor Field Theories: Renormalization and Random Geometry
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials