Flowing bosonization in the nonperturbative functional renormalization-group approach

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 $\phi$ and its conjugate partner, the phase $\vartheta$ 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 $\vartheta$ and $\phi$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$ 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 $\vartheta$ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field $\vartheta$ 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.

arXiv comment24 pages, 2 figures; v4) close to published version

References in corpus (36)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• An Introduction to the Nonperturbative Renormalization Group
• Flow Equations for N Point Functions and Bound States
• Chiral symmetry breaking in continuum QCD
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Renormalization Flow of Bound States
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Exact flow equation for composite operators
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Particle-hole fluctuations in the BCS-BEC Crossover
• Ultracold atoms and the Functional Renormalization Group
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Functional renormalization group approach to the BCS-BEC crossover
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Functional renormalization for quantum phase transitions with non-relativistic bosons
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Essential renormalisation group
• Non-perturbative renormalization-group approach to zero-temperature Bose systems
• Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
• Emergent Hadrons and Diquarks
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid
• Mott-glass phase of a one-dimensional quantum fluid with long-range interactions
• Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations
• Chaos in the Bose-glass phase of a one-dimensional disordered Bose fluid
• Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group
• Is there a Mott-glass phase in a one-dimensional disordered quantum fluid with linearly confining interactions?
• Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action

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