What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio

How does a quadratic term in the energy dispersion modify the single-particle Green's function of the Tomonaga-Luttinger model?

We calculate the effect of a quadratic term in the energy dispersion on the low-energy behavior of the Green's function of the spinless Tomonaga-Luttinger model (TLM). Assuming that for small wave-vectors q = k - k_F the fermionic excitation energy relative to the Fermi energy is v_F q + q^2 / (2m), we explicitly calculate the single-particle Green's function for finite but small values of lambda = q_c /(2k_F). Here k_F is the Fermi wave-vector, q_c is the maximal momentum transfered by the interaction, and v_F = k_F / m is the Fermi velocity. Assuming equal forward scattering couplings g_2 = g_4, we find that the dominant effect of the quadratic term in the energy dispersion is a renormalization of the anomalous dimension. In particular, at weak coupling the anomalous dimension is tilde{gamma} = gamma (1 - 2 lambda^2 gamma), where gamma is the anomalous dimension of the TLM. We also show how to treat the change of the chemical potential due to the interactions within the functional bosonization approach in arbitrary dimensions.Comment: 17 pages, 1 figur

Calculation of the average Green's function of electrons in a stochastic medium via higher-dimensional bosonization

The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our method is equivalent with conventional perturbation theory based on the lowest order Born approximation. For dynamic disorder, however, we obtain a new non-perturbative expression for the average Green's function. Bosonization also provides a solid microscopic basis for the description of the quantum dynamics of an interacting many-body system via an effective stochastic model with Gaussian probability distribution.Comment: RevTex, no figure

Tunnelling matrix elements with antiferromagnetic Gutzwiller wave functions

We use a generalized Gutzwiller Approximation (GA) elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic (AFM) order and obtain the corresponding tunnelling probabilities. The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo (VMC). Possible comparisons with experimental results are also discussed.Comment: 16 pages, 10 figure

Dynamic response of mesoscopic metal rings and thermodynamics at constant particle number

We show by means of simple exact manipulations that the thermodynamic persistent current $I ( \phi , N )$ in a mesoscopic metal ring threaded by a magnetic flux $\phi$ at constant particle number $N$ agrees even beyond linear response with the dynamic current $I_{dy} ( \phi , N )$ that is defined via the response to a time-dependent flux in the limit that the frequency of the flux vanishes. However, it is impossible to express the disorder average of $I_{dy} ( \phi , N )$ in terms of conventional Green's functions at flux-independent chemical potential, because the part of the dynamic response function that involves two retarded and two advanced Green's functions is not negligible. Therefore the dynamics cannot be used to map a canonical average onto a more tractable grand canonical one. We also calculate the zero frequency limit of the dynamic current at constant chemical potential beyond linear response and show that it is fundamentally different from any thermodynamic derivative.Comment: 19 pages, postscript (uuencoded, compressed

Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

We calculate the dynamic structure factor S (omega, q) of spinless fermions in one dimension with quadratic energy dispersion k^2/2m and long range density-density interaction whose Fourier transform f_q is dominated by small momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and k_F is the Fermi momentum. Using functional bosonization and the known properties of symmetrized closed fermion loops, we obtain an expansion of the inverse irreducible polarization to second order in the small parameter q_0 / k_F. In contrast to perturbation theory based on conventional bosonization, our functional bosonization approach is not plagued by mass-shell singularities. For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4) with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} | separates two regimes characterized by a different q-dependence of the width gamma_q of the collective zero sound mode and other features of S (omega, q). For q_c << q << k_F we find that the line-shape in this regime is non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a threshold singularity at the lower edge.Comment: 33 Revtex pages, 17 figure

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each RG step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Sigma (k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Sigma (k) = k_c^2 sigma^{-} (k | xi, k / k_c), where xi is the order parameter correlation length, k_c is the Ginzburg scale, and sigma^{-} (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.Comment: 9 pages, 4 figures, puplished versio

An Exactly Solvable Model of N Coupled Luttinger Chains

We calculate the exact Green function of a special model of N coupled Luttinger chains with arbitrary interchain hopping t_{perp}. The model is exactly solvable via bosonization if the interchain interaction does not fall off in the direction perpendicular to the chains. For any finite N we find Luttinger liquid behavior and explicitly calculate the anomalous dimension gamma^(N). However, the Luttinger liquid state does not preclude coherent interchain hopping. We also show that gamma^(N) -> 0 for N -> infinity, so that in the limit of infinitely many chains we obtain a Fermi liquid.Comment: accepted for publication in Phys. Rev.

Critical behavior of weakly interacting bosons: A functional renormalization group approach

We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional renormalization group, we calculate the universal scaling function for the self-energy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the four-point level. The self-energy interpolates between the critical regime k > k_c, where k_c is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior Sigma(k) \propto k^{2 - eta}, and in the short-wavelength regime the behavior is Sigma(k) \propto k^{2(D-3)} in D>3. In D=3, we recover the logarithmic divergence Sigma(k) \propto ln(k/k_c) encountered in perturbation theory. Our approach yields the crossover scale k_c as well as a reasonable estimate for the critical exponent eta in D=3. From our scaling function we find for the interaction-induced shift in T_c in three dimensions, Delta T_c / T_c = 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density, in excellent agreement with other approaches. We also discuss the flow of marginal parameters in D=3 and extend our truncation scheme of the renormalization group equations by including the six- and eight-point vertex, which yields an improved estimate for the anomalous dimension eta \approx 0.0513. We further calculate the constant lim_{k->0} Sigma(k)/k^{2-eta} and find good agreement with recent Monte-Carlo data.Comment: 23 pages, 7 figure