We re-visit the issue of the temperature dependence of the specific heat C(T) for interacting fermions in 1D. The charge component C_c(T) scales linearly with T, but the spin component C_s (T) displays a more complex behavior with T as it depends on the backscattering amplitude, g_1, which scales down under RG transformation and eventually behaves as g_1 (T) \sim 1/\log T. We show, however, by direct perturbative calculations that C_s(T) is strictly linear in T to order g^2_1 as it contains the renormalized backscattering amplitude not on the scale of T, but at the cutoff scale set by the momentum dependence of the interaction around 2k_F. The running amplitude g_1 (T) appears only at third order and gives rise to an extra T/\log^3 T term in C_s (T). This agrees with the results obtained by a variety of bosonization techniques. We also show how to obtain the same expansion in g_1 within the sine-Gordon model.
Fermi liquid theory of electronic topological transitions and screening anomalies in metals
给出了电子态密度中的Van Hove奇点（VHS）对Lifshitz电子拓扑跃迁（ETT）引起的热力学势$Ωare obtained in the framework of microscopic Fermi liquid theory. The renormalization of the singularities in $ Ω的贡献的一般表达式，并考虑了VHS与费米能级之间虚跃迁引起的屏蔽异常.结果表明，与ETT的单粒子图象相反，对于相互作用的电子，$Ω中的奇性是双侧的。
A unified theory for the cuprates, iron-based and similar superconducting systems: non-Fermi-liquid to Fermi-liquid crossover, low-energy and waterfall anomalies
Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2x2H2O and Observation of the Suppression and Re-entrance of Specific Heat Anomalies in Volborthite Under External Magnetic Field
