Flowing bosonization in the nonperturbative functional renormalization-group approach
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 ' and its conjugate partner, the phase # of the superfluid order parameter. We discuss the implem...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SciPost Foundation
2022
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| Online Access: | View Fulltext in Publisher |
| Summary: | 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 ' and its conjugate partner, the phase # 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 # and ' to remain conjugate variables at all energy scales, one must dynamically redefine the field # 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 # from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field # 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. © 2022 SciPost Foundation. All rights reserved. |
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| ISBN: | 25424653 (ISSN) |
| DOI: | 10.21468/SciPostPhys.12.3.110 |