Effective field theory of interactions on the lattice

Abstract

We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.

7 pages, 0 figures

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• New Trends in Density Matrix Renormalization
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Cited by in corpus (16)

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• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Quantum Simulation of Abelian Lattice Gauge Theories via State-Dependent Hopping
• Universal duality transformations in interacting one-dimensional quantum systems
• Stretching p-wave molecules by transverse confinements
• Three-body repulsive forces among identical bosons in one dimension
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• Anomalous frequency shifts in a one-dimensional trapped Bose gas
• Ion-induced interactions in a Tomonaga-Luttinger liquid
• Duality between weak and strong interactions in quantum gases
• Few-Body Route to One-Dimensional Quantum Liquids
• Ground-state properties of dilute spinless fermions in fractional dimensions
• Ultracold atoms in quasi-1D traps: a step beyond the Lieb-Liniger model
• Fermionic Luttinger liquids from a microscopic perspective
• Universality and tails of long range interactions in one dimension