Consistent regularization and renormalization in models with inhomogeneous phases

Abstract

In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

11 pages, no figures, agrees with published version

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Cited by in corpus (8)

• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Inhomogeneous chiral condensate in the quark-meson model
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Chiral density wave versus pion condensation in the 1+1 dimensional NJL model
• Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions $1\le d<3$
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter