Low-Temperature Anomaly of Electron-Spin Resonance in Dilute Alloys

Spencer, H. J.; Doniach, S.

doi:10.1103/physrevlett.18.994

Cited by 55 publications

(35 citation statements)

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“…(3), that the combination a † σ x behaves like a boson operator within each subspace E ± . To show this rigorously, we first take a drone-fermion representation [21] …”

Section: Introductionmentioning

confidence: 99%

Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

Hwang

Choi²

2010

Phys. Rev. A

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The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.

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“…(3), that the combination a † σ x behaves like a boson operator within each subspace E ± . To show this rigorously, we first take a drone-fermion representation [21] …”

Section: Introductionmentioning

confidence: 99%

Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

Hwang

Choi²

2010

Phys. Rev. A

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“…The calculation of these quantities requires a knowledge of both the four-leg vertex and the single-particle Green's function. Typically, the vertex is simply neglected, or treated in a very approximate fashion.An alternative approach is to take advantage of the anticommuting properties of Pauli matrices, writing the spin operator in terms of Majorana fermions [6,7,8,9,10],where η = (η 1 , η 2 , η 3 ) is a triplet of Majorana fermions which satisfy {η a , η b } = δ ab . This representation does not require the imposition of a constraint: the fact that S 2 = 3/4 follows directly from the operator properties of the Majorana fermions.…”

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Spin Dynamics from Majorana Fermions

et al. 2003

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Using the Majorana fermion representation of spin-1/2 local moments, we show how it is possible to directly read off the dynamic spin correlation and susceptibility from the one-particle propagator of the Majorana fermion. We illustrate our method by applying it to the spin dynamics of a nonequilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltagedependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B 66, 085315 (2002)].PACS numbers: 03.65. Ca, 72.15.Qm, 73.63.Kv, 76.20.+q The mathematical difficulties of representing spins in many body physics have long been recognized. The essence of the problem is that spin operators are nonabelian: they do not obey Wick's theorem and an expectation value of the product of many spin operators cannot be decomposed into products of two-operator expectation values, even within a free theory.A conventional response to this difficulty is to represent spins as bilinears of fermions [1] or as bosons [2]. One of the disadvantages of these approaches is that the Hilbert space of the fermions or bosons needs to be restricted by the application of constraints [3,4,5]. Another difficulty is the "vertex problem", which arises in the context of spin dynamics and spin relaxation. Once the spins are represented as bilinears, the spin-spin correlation functions are represented by two-particle Green's functions. The calculation of these quantities requires a knowledge of both the four-leg vertex and the single-particle Green's function. Typically, the vertex is simply neglected, or treated in a very approximate fashion.An alternative approach is to take advantage of the anticommuting properties of Pauli matrices, writing the spin operator in terms of Majorana fermions [6,7,8,9,10],where η = (η 1 , η 2 , η 3 ) is a triplet of Majorana fermions which satisfy {η a , η b } = δ ab . This representation does not require the imposition of a constraint: the fact that S 2 = 3/4 follows directly from the operator properties of the Majorana fermions. In this letter, we show how this representation also solves the vertex problem. To demonstrate this, we employ an alternative derivation [11] of the Majorana spin representation. Consider a spin-1/2 operator S with dynamics described by a Hamiltonian H. Let us now introduce a single Majorana fermion Φ which lives in a completely different Hilbert space, commuting with S and H. It follows that Φ is a fermionic constant of motion, dΦ/dt = −i[H, Φ] = 0: an object of fixed magnitude Φ 2 = 1/2 which anticommutes with all other fermion operators. We may now identify η in (1) with the operator identityWe may confirm that {η a , η b } = δ ab using the anticommuting algebra of spin-1/2 operators {S a , S b } = 1 2 δ ab . Furthermore, using the SU(2) algebra of spins, η × η = 2 S × S = 2i S, from which (1) follows immediately. As a last step in the derivation, we note tha...

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“…(1) is the 'drone' (Majorana) fermion representation [11],σ + =ĉ †φ ,σ z = 2ĉ †ĉ − 1. whereφ =d † +d is a Majorana fermion andĉ andd are Dirac fermions. This formulation enables one to apply Wick's theorem and the fermionic Schwinger-Keldysh approach [12,13].…”

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confidence: 99%

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

2006

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We evaluate the current distribution for a single-electron transistor with intermediate strength tunnel conductance. Using the Schwinger-Keldysh approach and the drone (Majorana) fermion representation we account for the renormalization of system parameters. Nonequilibrium effects induce a lifetime broadening of the charge-state levels, which suppress large current fluctuations. PACS numbers: 73.23.Hk,72.70.+m The 'Full Counting Statistics' (FCS) of charge transport has proven to be a powerful tool in the description of current fluctuations [1]. The concept had been explored by Levitov and Lesovik [2], who expressed the FCS of an arbitrary mesoscopic structure with non-interacting electrons in terms of its S−matrix. Much less is known about the FCS of interacting mesoscopic systems, a problem which has been addressed only recently [3,4,5,6,7].As a fundamental example of an interacting mesoscopic systems we consider a Single-Electron Transistor (SET). It consists of a metallic island coupled to drain and source (left and right) electrodes via low-capacitance tunnel junctions, with resistances R L and R R , as well as to a gate electrode. The strength of Coulomb interaction is characterized by the charging energy E C = e 2 /2C Σ , which depends on the total capacitance C Σ = C L +C R +C G . A measure for the tunneling strength is the dimensionlessIn Refs. [3,4] the FCS of a similar system -a quantum dot -has been studied, fully accounting for strong electron correlations, however only for a particular setup and parameters, corresponding to the Toulouse point. A renormalization group approach had been developed for the regime α 0 ≫ 1 [5]. In the opposite limit, α 0 → 0, the FCS has been analyzed to lowest order in Ref.[6] and next-to-lowest order (cotunneling) in Ref. [7]. However, effects of quantum fluctuations induced by nonvanishing α 0 are still unknown. The aim of the present paper is to derive the FCS for a SET beyond perturbation theory in the intermediate strength tunneling regime α 0 1.Let us further specify the situation to be considered. At low transport voltages and temperatures, eV, T ≪ E C , due to Coulomb blockade tunneling is suppressed in a SET, everywhere except near specific values of the gate voltage, e.g., near Q G ≡ C G V G = e/2. In the neighborhood of this conductance peak the Coulomb barrier is ∆ 0 = E C (1 − 2Q G /e). For α 0 ≪ 1 electrons tunnel via the island sequentially only when µ R < ∆ 0 < µ L , where µ L/R = κ L/R eV is the voltage drop between the L/R electrode and the island, andWith increasing α 0 , higher order effects such as cotunneling and quantum fluctuations of the charge gain importance [8]. They lead to a renormalization of ∆ 0 and α 0 . The perturbative renormalization group analysis [9] (for eV = 0) predicts a renormalization factor z 0 = 1/{1 + 2α 0 ln(E C /Λ)} to depend logarithmically on the cutoff energy Λ = max{∆ 0 , T }.The model. -We concentrate on the tunneling regime with inverse RC time 1/R T C Σ = 4πα 0 E C smaller than E C , which ensures that the charge...

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Low-Temperature Anomaly of Electron-Spin Resonance in Dilute Alloys

Cited by 55 publications

References 10 publications

Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

Spin Dynamics from Majorana Fermions

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

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