Renormalization in condensed matter: Fermionic systems – from mathematics to materials

  title={Renormalization in condensed matter: Fermionic systems – from mathematics to materials},
  author={Manfred Salmhofer},
  journal={Nuclear Physics B},
The nonperturbative functional renormalization group and its applications
Partial bosonization for the two-dimensional Hubbard model
Partial bosonisation of the two-dimensional Hubbard model focuses the functional renormalisation flow on channels in which interactions become strong and local order sets in. We compare the momentum
Tensor Field Theories : Renormalization and Random Geometry
This thesis divides into two parts, focusing on the renormalization of quantum field theories. The first part considers three tensor models in three dimensions, a fermionic quartic with tensors of
Investigation of supersymmetry on a strongly-interacting Majorana zero mode chain
Majorana fermions have been an important subject of research for the past few years in the field of condensed matter physics. After the realization of Majorana zero mode (MZM) in a Kitaev-chain,
QMeS-Derivation: Mathematica package for the symbolic derivation of functional equations
We present the Mathematica package QMeS-Derivation. It derives symbolic functional equations from a given master equation. The latter include functional renormalisation group equations,


We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained
Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds
An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green’s functions of
Massless lattice φ44 theory: Rigorous control of a renormalizable asymptotically free model
Using block spin renormalization group techniques, we rigorously control the functional integral of a weakly coupled critical latticeφ4 theory in four euclidean dimensions proving the infrared
Renormalization group approach to lattice gauge field theories
We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized
Interacting Fermi Liquid in Two Dimensions at Finite Temperature. Part II: Renormalization
Abstract: This is a companion paper to [DR1]. Using the method of continuous renormalization group around the Fermi surface and the results of [DR1], we achieve the proof that a two-dimensional
An inversion theorem in Fermi surface theory
We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and
Continuous Renormalization for Fermions and Fermi Liquid Theory
Abstract:I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the
A low temperature expansion for classicalN-vector models. II. Renormalization group equations
This paper continues the analysis of the low temperature expansions for classicalN-vector models started in [1]. A main part of it is a derivation of renormalization group equations and a
Fermionic Renormalization Group Flows: Technique and Theory
We give a self-contained derivation of the differential equations for Wilson’s renormalization group for the one-particle irreducible Green functions in fermionic systems. The application of this
Perturbative Renormalizability of 3 by renormalization group differential equations
I discuss the setup and details of proofs of perturbative renormalizability by renormalization group differential equations. As an example, I show that 3 theory in six dimensions is perturbatively