Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Temperature-Squared Term in the Heat Capacity of a Two-Dimensional Fermi Liquid

節夫 三沢

Published Jul 15, 1999• 19 citations
Publisher

Abstract

The spin susceptibility of a two-dimensional (2D) Fermi liquid has been recently shown, by Hirashima and Takahashi [J. Phys. Soc. Jpn. 67 (1998) 3816], to vary as χ( T )=χ 0 +α T as a function of temperature T , where χ 0 and α are constants. From the analytic form of the free energy which is compatible with this χ and the third law of thermodynamics, we can deduce that the entropy S , and hence the heat capacity, of the system varies as T 2 . This T 2 -term of S is also compatible with the theoretical prediction for the self-energy part of the 2D quasiparticles.

DOI
10.1143/jpsj.68.2172

Related papers

Thermodynamics of a Fermi Liquid beyond the Low-Energy Limit

Andrey V. Chubukov, Dmitrii L. Maslov, Suhas Gangadharaiah +1 more

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.

arXiv:cond-mat/0502542•Physical Review Letters•Jul 8, 2005•36 citations

Quasiparticle spectra and the calculation of thermodynamics for a two-dimensional Fermi liquid

Dermot Coffey

If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the ${\mathit{T}}^{3}$lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.

Physical review. B, Condensed matter•May 15, 1995•1 citation

Thermodynamics of the nonrelativistic free-electron Fermi gas in one, two, and three dimensions from the degenerate to the nondegenerate temperature regime

D. C. Johnston

The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.

arXiv:2012.07663•Dec 14, 2020•1 citation

First temperature corrections to the Fermi-liquid fixed point in two dimensions

Gennady Y. Chitov, Andrew J. Millis

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 $T=0$ 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.

arXiv:cond-mat/0103155•Physical review. B, Condensed matter•Jul 11, 2001•44 citations

Quasiparticle Weight of the Two-Dimensional Hubbard Model in thet-Matrix Approximation

Osamu Narikiyo

The quasiparticle weight of the two-dimensional Hubbard model in thet-matrix approximation is discussed in comparison with a recent report by Yokoyama and Fukuyama (J. Phys. Soc. Jpn. 66 (1997), 529) where the breakdown of the quasiparticle description of the Fermi liquid was concluded.

Progress of Theoretical Physics•Jun 1, 1997•1 citation

Leading Temperature Corrections to Fermi-Liquid Theory in Two Dimensions

Gennady Y. Chitov, Andrew J. Millis

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.

arXiv:cond-mat/0101399•Physical Review Letters•Jun 4, 2001•44 citations
The spin susceptibility of a two-dimensional (2D) Fermi liquid has been recently shown, by Hirashima and Takahashi [J. Phys. Soc. Jpn. 67 (1998) 3816], to vary as χ( T )=χ 0 +α T as a function of temperature T , where χ 0 and α are constants. From the analytic form of the free energy which is compatible with this χ and the third law of thermodynamics, we can deduce that the entropy S , and hence the heat capacity, of the system varies as T 2 . This T 2 -term of S is also compatible with the theoretical prediction for the self-energy part of the 2D quasiparticles.
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.
If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the T3{\mathit{T}}^{3}T3lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.
The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.
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.
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.