arXiv:2111.11458 · SciPost Physics

Flowing bosonization in the nonperturbative functional renormalization-group approach

Romain Daviet, N. Dupuis

Published Mar 28, 2022• 6 citations

Abstract

Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the ``density’’ field \varphi φ and its conjugate partner, the phase \vartheta ϑ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for \vartheta ϑ and \varphi φ to remain conjugate variables at all energy scales, one must dynamically redefine the field \vartheta ϑ along the renormalization-group flow. We derive explicit flow equations using a derivative expansion of the scale-dependent effective action to second order and show that they reproduce the flow equations of the sine-Gordon model (obtained by integrating out the field \vartheta ϑ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field \vartheta ϑ do we obtain the standard phenomenology of the Luttinger liquid (when the periodic potential is sufficiently weak so as to avoid the Mott-insulating phase) characterized by two low-energy parameters, the velocity of the sound mode and the renormalized Luttinger parameter.

DOI: 10.21468/scipostphys.12.3.110

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