Interweaving Chiral Spirals

Details Interweaving Chiral Spirals Interweaving Chiral Spirals

2011-07-11

arxiv.org/abs/1107.2124v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

52 pages, 18 figures

Scientific paper

We elaborate how to construct the interweaving chiral spirals in (2+1) dimensions, that is defined as a superposition of differently oriented chiral spirals. We divide the two-dimensional Fermi sea into distinct wedges characterized by the opening angle 2 Theta and the depth Q \simeq pF, where pF is the Fermi momentum. Each wedge earns an energy gain by forming a single chiral spiral. The optimal values for Theta and Q are chosen by the balance between this energy gain and the energy costs from the deformed Fermi surface (dominant at large Theta) and patch-patch interactions (dominant at small Theta). We estimate these energy gains and costs by means of the expansions in terms of 1/Nc, Lambda_QCD/Q, and Theta using a non-local four-Fermi interaction model: At small 1/Nc the mass gap (chiral condensate) is large enough and the interaction among quarks and the condensate is local in momentum space thanks to the form factor in our non-local model. The fact that patch-patch interactions lie only near the patch boundaries makes it simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and formulate the perturbation theory in terms of subdominant terms suppressed by Lambda_QCD/Q or Theta. The kinetic term in the transverse directions turns out to be subdominant, so that we can utilize techniques in the (1+1)-dimensional system. Our central results at the leading order of the 1/Nc and the Lambda_QCD/Q expansions are that the total energy gain is \sim pF Lambda_QCD^2 with Theta \sim (Lambda_QCD/pF)^{3/5}. Since Theta decreases with increasing pF, there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large-Nc approximation is more reliable.

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