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arXiv:1404.5655 · Nuclear Physics A

Approaching Pomeranchuk instabilities from ordered phase: A crossing-symmetric equation method

Kelly Reidy, Khandker Quader, Kevin S. Bedell

Published May 22, 2014• 1 citation
arXivHTMLPDF
DOI
10.1016/j.nuclphysa.2014.05.012

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Features of Fermi Systems near ℓ\ellℓ=0 Pomeranchuk Instabilities: A Crossing Symmetric Approach
We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except l=1l=1l=1 can take place if the interaction is repulsive and has a finite range r0{r}_{0}r0​ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.
We present a stability analysis of the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for various values of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}},$ and electron concentrations close to the Van Hove filling by means of the flow equation method. For ${t}^{\ensuremath{'}}>~\ensuremath{-}t/3$ a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave Pomeranchuk instability dominates (apart from antiferromagnetism at small ${t}^{\ensuremath{'}}).$ At ${t}^{\ensuremath{'}}<\ensuremath{-}t/3,$ the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures T<0.15t,T<0.15t,T<0.15t, and an s∗{s}^{*}s∗-magnetic phase for T>0.15t;T>0.15t;T>0.15t; upon increasing the electron concentration, the triplet analog of the flux phase occurs at low temperatures. Other weaker instabilities are also found.