Thermodynamics of a Fermi liquid in a magnetic field

Betouras, Joseph J.; Efremov, D. V.; Chubukov, Andrey V.

doi:10.1103/physrevb.72.115112

Cited by 39 publications

(77 citation statements)

References 25 publications

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“…They performed a perturbative calculation of the momentumdependent spin susceptibility χ s (Q, T = 0) at small Q and found a non-analytic Q 2 ln Q behavior. Later, it was found [30] that the magnetic-field dependence of a nonlinear spin susceptibility parallels the Q-dependence, i.e., χ s (Q = 0, T = 0, H) ∝ H 2 ln |H|. Nonanalyticity of the spin susceptibility was also found for 2D systems by Millis and Chitov [24] and, later, Chubukov and Maslov [27], Galitski et al [29], and Betouras et al [30].…”

Section: Spin Susceptibility In 3dmentioning

confidence: 82%

“…On the other hand the previous 3D work [12,15,16] found no special role of backscattering for the T 2 ln T nonanalyticity. (iii) The older work left the impression that in 3D the nonanalyticities were particular to γ and did not contribute to susceptibilities, whereas more recent work (based mainly on perturbative calculations) has demonstrated that nonanalytic corrections to the spin susceptibility occur both in 3D [21] and in 2D [24,25,26,27,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

“…For interacting fermions, γ(T ) is not an analytic function of T 2 ; the leading temperature dependence is instead proportional to T 2 ln(T ) in three dimensions (3D) and T in 2D The T 2 ln T term was first found by Eliashberg in a theoretical study of electrons interacting with acoustic phonons [5], and the possibility of a nonanalytic temperature dependence of γ was subsequently (but apparently independently) inferred from measurements of γ for 3 He by Abel, Wheately and Andersen [1]. The 3 He measurements led to a large literature [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] which we review in detail below. We note here a few crucial (and seemingly contradictory) results.…”

Section: Introductionmentioning

confidence: 99%

“…The thermodynamic properties of itinerant fermionic systems is a subject of long-standing experimental [1,2,3] and theoretical [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] interest. It is generally accepted [31,32] that the low-temperature behavior of a wide class of interacting fermionic systems is controlled by the Fermi-liquid fixed point.…”

Section: Introductionmentioning

confidence: 99%

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Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid

2006

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We revisit the issue of the leading nonanalytic corrections to the temperature dependence of the specific heat coefficient, γ(T ) = C(T )/T, for a system of interacting fermions in three dimensions. We show that the leading temperature dependence of the specific heat coefficient γ(T ) − γ(0) ∝ T 3 ln T comes from two physically distinct processes. The first process involves a thermal excitation of a single particle-hole pair, whose components interact via a nonanalytic dynamic vertex. The second process involves an excitation of three particle-hole pairs which interact via the analytic static fixed-point vertex. We show that the single-pair contribution is expressed via the backscattering amplitude of quasiparticles at the Fermi surface. The three-pair contribution does not have a simple expression in terms of scattering in particular directions. We clarify the relation between these results and previous literature on both 3D and 2D systems, and discuss the relation between the nonanalyticities in γ and those in spin susceptibilities.

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Section: Spin Susceptibility In 3dmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid

2006

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“…Evaluating the sum one finds that Ω 2 contains a cross term T H 2 [13]. Differentiating over frequency, one then obtains δχ s (T ) ∝ T , as in (1).…”

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confidence: 99%

Temperature-dependent spin susceptibility in a two-dimensional metal

2005

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We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature T . We show that the dynamic Kohn anomaly in the response function at 2k F leads to a non-analytic, linear-in-T correction to the spin susceptibility, δχ(T ) = AT , same as in systems with short-range interaction. We show that the singularity of the Coulomb interaction at q = 0 does not invalidate the expansion of A in powers of r s , but makes the expansion non-analytic. We argue that the linear temperature dependence is consistent with the general structure of Landau theory and can be viewed as originating from the non-analytic component of the Landau function near the Fermi surface.Introduction -There has been substantial recent interest in the temperature dependence of various Fermi liquids properties for both short-range and long-range interactions between particles [1,2,3,4,5,6]. The revival of interest in the problem is two-fold. On the experimental side, technical advances now allow one to measure the temperature dependence of the thermodynamic parameters such as specific heat and spin susceptibility in "classical" 2D Fermi liquids with short-range interaction, such as monolayers of 3 He, as well as study twodimensional semiconductor structures with long-range interaction and with relatively low Fermi temperatures (∼ 1 K). On the theory side, the leading interaction corrections turn out to be non-analytic functions of temperature making the subject particularly important.Naïve power counting arguments suggest that the temperature dependence of any thermodynamic quantity, including the spin susceptibility and the specific heat coefficient C(T )/T = γ, should start with terms quadratic in temperature. This conjecture is based on the observation that a thermodynamic quantity at a finite temperature typically can be written as a(ε)n(ε)dε, where n(ε) is the Fermi distribution function and a(ε) is some function. If the latter is smooth, the temperature dependence starts with a term of order T 2 [7]. Such a temperature correction is called "analytic." This is also consistent with the intuitive expectation of the one-to-one correspondence between the non-interacting Fermi gas and the interacting Fermi liquid since in the Fermi gas, the Sommerfeld expansion leads to simple quadratic temperature corrections.However, the assumption about the analyticity of the functions involved in the calculation of various thermodynamic properties of the Fermi liquid is quite generally not justified because in any Fermi liquid, the dynamic interaction between particles gives rise to a non-analytic energy dependence of a(ε). This leads to temperature corrections which do not scale as T 2 and are therefore called "non-analytic." Collecting these non-analytic corrections is a subtle theoretical problem.The subject of this paper is the temperature correction to the spin susceptibility for a 2D system of fermions interacting via a long-range Coulomb interaction. For Fermi systems with short-range interaction, perturbative c...

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The quantum ferromagnetic transition in a clean Kondo lattice is discontinuous

Kirkpatrick

Belitz

2016

Fortschritte der Physik

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The Kondo-lattice model, which couples a lattice of localized magnetic moments to conduction electrons, is often used to describe heavy-fermion systems. Because of the interplay between Kondo physics and magnetic order it displays very complex behavior and is notoriously hard to solve. The ferromagnetic Kondo-lattice model, with a ferromagnetic coupling between the local moments, describes a phase transition from a paramagnetic phase to a ferromagnetic one as a function of either temperature or the ferromagnetic local-moment coupling. At zero temperature, this is a quantum phase transition that has received considerable attention. It has been theoretically described to be continuous, or second order. Here we show that this belief is mistaken; in the absence of quenched disorder the quantum phase transition is first order, in agreement with experiments, as is the corresponding transition in other metallic ferromagnets.

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Thermodynamics of a Fermi liquid in a magnetic field

Cited by 39 publications

References 25 publications

Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid

Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid

Temperature-dependent spin susceptibility in a two-dimensional metal

The quantum ferromagnetic transition in a clean Kondo lattice is discontinuous

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