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arXiv:cond-mat/0304189 · Physical review. B, Condensed matter

Renormalization group analysis of magnetic and superconducting instabilities near van Hove band fillings

A. A. Katanin, A. P. Kampf

Published Nov 3, 2003• 83 citations
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Abstract

Phase diagrams of the two-dimensional one-band $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model are obtained within the two-patch and temperature-cutoff many-patch renormalization group approaches. At small ${t}^{\ensuremath{'}}$ and at van Hove band fillings antiferromagnetism dominates, while with increasing ${t}^{\ensuremath{'}}$ or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near ${t}^{\ensuremath{'}}=t/2$ and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.

DOI
10.1103/physrevb.68.195101

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The phase diagram of the two-dimensional extended one-band $U\ensuremath{-}V\ensuremath{-}J$ Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization-group (RG) approaches near the Van Hove band fillings. At small ${t}^{\ensuremath{'}}$ and J>0,J>0,J>0, mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach that predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. There is a complex competition between SDW, CF phases, and d-wave superconductivity at small ${t}^{\ensuremath{'}}$ in two- and many-patch RG approaches. The spin-flux phase, which is not stable at the mean-field level, is identified as a possible ground state at J<0J<0J<0 in both RG approaches. With increasing ${t}^{\ensuremath{'}}$ the results of all three approaches merge: d-wave superconductivity at J>0J>0J>0 and ferromagnetism at J<0J<0J<0 become the leading instabilities. For large enough V, the charge-density-wave state occurs.
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional ${t\ensuremath{-}t}^{\ensuremath{'}}$ Hubbard model for particle densities close to the Van Hove filling as a function of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. In the one-loop flow at the Van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around ${t}_{c}^{\ensuremath{'}}\ensuremath{\approx}\ensuremath{-}0.33t$, suggesting a quantum critical point between ddd-wave pairing at moderate ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ and ferromagnetism for ${t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$. Upon increasing the particle density in the latter regime, the leading instability occurs in the triplet pairing channel.
We study a ferromagnetic tendency in the two-dimensional Hubbard model near van Hove filling by using a functional renormalization-group method. We compute temperature dependences of magnetic susceptibilities including incommensurate magnetism. The ferromagnetic tendency is found to occur in a dome-shaped region around van Hove filling with an asymmetric property: incommensurate magnetism is favored near the edge of the dome above van Hove filling whereas a first-order-like transition to the ferromagnetic ground state is expected below van Hove filling. The dome-shaped phase diagram is well captured in the Stoner theory by invoking a smaller Coulomb interaction. Triplet p-wave superconductivity tends to develop at low temperatures inside the dome and extends more than the ferromagnetic region above van Hove filling.
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.