de Alcantara Bonfim and Reiter reply

Bonfim, O. F. de Alcantara; Reiter, George

doi:10.1103/physrevlett.70.249

Cited by 48 publications

(72 citation statements)

References 3 publications

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“…In this situation, typicality can provide a fresh numerical perspective [9], Much less is known on transport dynamics apart from the mere existence of Drude weights. For spin transport at A = 1, steady-state bath scenarios [61,62] and classical simulations [63][64][65] suggest superdiffusive dynamics in the limit of high temperatures, while bosonization predicts diffusion at low but nonzero temperatures [66]. At A > 1, signatures of diffusion have been observed also at high temperatures in different approaches [47,61,62,65,67,68] (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Spin and energy currents in integrable and nonintegrable spin-12chains: A typicality approach to real-time autocorrelations

2015

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We use the concept of typicality to study the real-time dynamics of spin and energy currents in spin-1 /2 models in one dimension and at nonzero temperatures. These chains are the integrable XXZ chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in the z direction. In the framework of linear response theory, we numerically calculate autocorrelation functions by propagating a single pure state, drawn at random as a typical representative of the full statistical ensemble. By comparing to small-system data from exact diagonalization (ED) and existing short-time data from time-dependent density matrix renormalization group, we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both integrable and nonintegrable systems. For the integrable case, we calculate the long-time dynamics of the spin current and extract the spin Drude weight for large systems outside the range of ED. We particularly provide strong evidence that the high-temperature Drude weight vanishes at the isotropic point. For the nonintegrable case, we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field, exchange anisotropy, and temperature.

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Section: Introductionmentioning

confidence: 99%

Spin and energy currents in integrable and nonintegrable spin-12chains: A typicality approach to real-time autocorrelations

2015

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“…In particular, it was found that the usual hydrodynamic assumptions break down in one dimension, so that the asymptotic behavior of the spin-spin correlation function deviates from the predictions of the classical diffusion theory ͑see Ref. 5 and references therein͒.…”

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confidence: 99%

Spin diffusion in one-dimensional antiferromagnets

Narozhny

1996

Phys. Rev. B

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We study the problem of spin diffusion in magnetic systems without long-range order. We discuss the example of the one-dimensional spin chain. For the system described by the Heisenberg Hamiltonian we show that there are no diffusive excitations. However, the addition of an arbitrarily small dissipation term, such as the spin-phonon interaction, leads to diffusive excitations in the long-time limit. For those excitations we estimate the spin-diffusion coefficient by means of the renormalization group analysis. ͓S0163-1829͑96͒01330-6͔

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“…We computed several logarithms of r to check the above scaling theory and found agreement with calculations of the critical exponents in the critical (massless) phase [14]. The most important result comes from the second order (two-loop) coefficient of x 3 log r that provides the temperature exponent of the slope a of Q(x) showing that it is equal to β, at least up to O(ǫ).…”

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confidence: 89%

“…They did not find any meaningful fixpoint, thus suggesting that there is no ATline around 6 dimensions. We feel, however, that their projected field theory, with all the masses other than that of the replicon taken to be infinite, is not sufficient to settle the question since even the crossover region including the known zero-field fixed-point [14] is impossible to reach in this model with only two cubic coupling constants. Taking into account all the eight cubic invariants of the permutation group we would have a large enough parameter space with eight ϕ 3 coupling constants and three masses.…”

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confidence: 99%

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Scaling and infrared divergences in the replica field theory of the Ising spin glass

1999

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Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d = 6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w 2 . Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the ǫ-expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w 2 and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed.Spin glasses [1] have posed a formidable theoretical challenge ever since Edwards and Anderson [2] proposed their simple looking model containing the two basic features of disordered systems: randomness and frustration.

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de Alcantara Bonfim and Reiter reply

Cited by 48 publications

References 3 publications

Spin and energy currents in integrable and nonintegrable spin-12chains: A typicality approach to real-time autocorrelations

Spin and energy currents in integrable and nonintegrable spin-12chains: A typicality approach to real-time autocorrelations

Spin diffusion in one-dimensional antiferromagnets

Scaling and infrared divergences in the replica field theory of the Ising spin glass

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