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arXiv:cond-mat/0101399 · Physical Review Letters

Leading Temperature Corrections to Fermi-Liquid Theory in Two Dimensions

Gennady Y. Chitov, Andrew J. Millis

Published Jun 4, 2001• 44 citations
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Abstract

We calculate the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the "charge-sector" quantities are found to cancel to second order in the interaction, but the cancellation is argued not to be generic. The connection with previous studies of the 2D Fermi-liquid parameters is discussed.

DOI
10.1103/physrevlett.86.5337

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We calculate the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the "charge-sector" quantities are found to cancel to second order in the interaction, but the cancellation is argued not to be generic. The connection with previous studies of the 2D Fermi-liquid parameters is discussed.
We calculate, using perturbative calculations and Ward identities, the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard T=0T=0T=0 relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.
The renormalization-group (RG) approach proposed earlier by Shankar for interacting spinless fermions at T=0 is extended to the case of nonzero temperature and spin. We study a model with SU(N)-invariant short-range effective interaction and rotationally invariant Fermi surface in two and three dimensions. We show that the Landau interaction function of the Fermi liquid, constructed from the bare parameters of the low-energy effective action, is RG invariant. On the other hand, the physical forward-scattering vertex is found as a stable fixed point of the RG flow. We demonstrate that in d=2 and 3, the RG approach to this model is equivalent to Landau's mean-field treatment of the Fermi liquid. We discuss subtleties associated with the symmetry properties of the scattering amplitude, the Landau function, and the low-energy effective action. Applying the RG to response functions, we find the compressibility and the spin susceptibility as fixed points.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
We consider the nonanalytic temperature dependences of the specific heat coefficient, C(T)/T, and spin susceptibility, chi(s)(T), of 2D interacting fermions beyond the weak-coupling limit. We demonstrate within the Luttinger-Ward formalism that the leading temperature dependences of C(T)/T and chi(s)(T) are linear in T, and are described by the Fermi liquid theory. We show that these temperature dependences are universally determined by the states near the Fermi level and, for a generic interaction, are expressed via the spin and charge components of the exact backscattering amplitude of quasiparticles. We compare our theory to recent experiments on monolayers of He3.
We show that the singularities in the dynamical bosonic response functions of a two-dimensional Fermi liquid give rise to universal nonanalytic corrections to the results of the Fermi-liquid theory. In particular, we find a T2{T}^{2}T2 term in the specific heat, linear-in-TTT terms in the effective mass and in the uniform spin susceptibility ${\ensuremath{\chi}}_{s}(Q=0,T),$ and ∣Q∣|Q|∣Q∣ term in ${\ensuremath{\chi}}_{s}(Q,T=0).$ The existence of these terms has been the subject of recent controversy, which is resolved in this paper. We present exact expressions for all nonanalytic terms to second order in a generic interaction U(Q)U(Q)U(Q) and show that the nonanalytic terms originate exclusively from forward- and backward-scattering of particles with zero total momentum.
We show that the singularities in the dynamical bosonic response functions of a two-dimensional Fermi liquid give rise to universal nonanalytic corrections to the results of the Fermi-liquid theory. In particular, we find a T2{T}^{2}T2 term in the specific heat, linear-in-TTT terms in the effective mass and in the uniform spin susceptibility ${\ensuremath{\chi}}_{s}(Q=0,T),$ and ∣Q∣|Q|∣Q∣ term in ${\ensuremath{\chi}}_{s}(Q,T=0).$ The existence of these terms has been the subject of recent controversy, which is resolved in this paper. We present exact expressions for all nonanalytic terms to second order in a generic interaction U(Q)U(Q)U(Q) and show that the nonanalytic terms originate exclusively from forward- and backward-scattering of particles with zero total momentum.