Second order functional renormalization group approach to one-dimensional systems in real and momentum space

Abstract

We devise a functional renormalization group treatment for a chain of interacting spinless fermions which is correct up to second order in the interaction strength. We treat both inhomogeneous systems in real-space as well as the translational invariant case in a k-space formalism. The strengths and shortcomings of the different schemes as well as technical details of their implementation are discussed. We use the method to study two proof-of-principle problems in the realm of Luttinger liquid physics, namely reflection at interfaces and power laws in the occupation number as a function of crystal momentum.

9 pages

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Cited by in corpus (4)

• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Detecting phases in one-dimensional many-fermion systems with the functional renormalization group
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Second-order functional renormalization group approach to quantum wires out of equilibrium