arXiv subjects

Peter Kopietz

Publications and source records attributed to Peter Kopietz.

At least 37 records · Page 2Linked to original sources

arXiv2021

Dissipative spin dynamics in hot quantum paramagnets

We use the functional renormalization approach for quantum spin systems developed by Krieg and Kopietz [Phys. Rev. B $\mathbf{99}$, 060403(R) (2019)] to calculate the spin-spin correlation function $G (\boldsymbol{k}, ω)$ of quantum Heisenberg magnets at infinite temperature. For small wavevectors $\boldsymbol{k} $ and frequencies $ω$ we find that $G ( \boldsymbol{k}, ω)$ assumes in dimensions $d > 2$ the diffusive form predicted by hydrodynamics. In three dimensions our result for the spin-diffusion coefficient ${\cal{D}}$ is somewhat smaller than previous theoretical predictions based on the extrapolation of the short-time expansion, but is still about $30 \%$ larger than the measured high-temperature value of ${\cal{D}}$ in the Heisenberg ferromagnet Rb$_2$CuBr$_4\cdot$2H$_2$O. In reduced dimensions $d \leq 2$ we find superdiffusion characterized by a frequency-dependent complex spin-diffusion coefficient ${\cal{D}} ( ω)$ which diverges logarithmically in $d=2$, and as a power-law ${\cal{D}} ( ω) \propto ω^{-1/3}$ in $d=1$. Our result in one dimension implies scaling with dynamical exponent $z =3/2$, in agreement with recent calculations for integrable spin chains. Our approach is not restricted to the hydrodynamic regime and allows us to calculate the dynamic structure factor $S ( \boldsymbol{k} , ω)$ for all wavevectors. We show how the short-wavelength behavior of $S ( \boldsymbol{k}, ω)$ at high temperatures reflects the relative sign and strength of competing exchange interactions.

cond-mat.stat-mech↗

arXiv2021

Effect of magnon decays on parametrically pumped magnons

We investigate the influence of magnon decays on the non-equilibrium dynamics of parametrically excited magnons in the magnetic insulator yttrium-iron garnet (YIG). Our investigations are motivated by a recent experiment by Noack et al. [Phys. Status Solidi B 256, 1900121 (2019)] where an enhancement of the spin pumping effect in YIG was observed near the magnetic field strength where magnon decays via confluence of magnons becomes kinematically possible. To explain the experimental findings, we have derived and solved kinetic equations for the non-equilibrium magnon distribution. The effect of magnon decays is taken into account microscopically via collision integrals derived from interaction vertices involving three powers of magnon operators. Our results agree quantitatively with the experimental data.

cond-mat.stat-mech↗

arXiv2021

Zero-magnon sound in quantum Heisenberg ferromagnets

Using a functional renormalization group approach we show that at low temperatures and in a certain range of magnetic fields the longitudinal dynamic structure factor of quantum Heisenberg ferromagnets in dimensions $D\leq 2$ exhibits a well-defined quasi-particle peak with linear dispersion that we identify as zero-magnon sound. In $D>2$ the larger phase space available for the decay into transverse spin waves leads only to a broad hump centered at zero frequency whose width scales linearly in momentum.

cond-mat.stat-mech↗

arXiv2020

Quantum discontinuity fixed point and renormalization group flow of the SYK model

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. This flow allows for an understanding of the surprising role of critical slowing down at a quantum first-order transition in strongly-correlated electronic systems. From a simple truncation of the infinite hierarchy of the exact functional RG flow equations we identify several fixed points: Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of this quantum first-order transition in terms of a local effective Ising variable that is established for classical transitions. It reveals that quantum phase coexistence can be a genuine critical state of matter.

cond-mat.str-el↗

arXiv2020

Collisionless kinetic theory for parametrically pumped magnons

We discuss collisionless kinetic equations describing the non-equilibrium dynamics of magnons in a ferromagnet exposed to an oscillating microwave field. Previously, this problem has been treated within the so-called "S-theory" where the collision integral in the kinetic equation for the magnon distribution is either neglected or taken into account phenomenologically via an effective relaxation time. However, the possibility of magnon condensation has not been included in S-theory. Moreover, the momentum integrations appearing in the magnon self-energies are usually decoupled by retaining only the term where the loop momentum is equal to the external momentum. In this work we critically examine the accuracy of these approximations and develop the proper extensions of S-theory. We show that these extensions can significantly modify the time evolution of the magnon distribution.

cond-mat.stat-mech↗

arXiv2019

Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions

We use the spin functional renormalization group recently developed by two of us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to calculate the magnetization $M ( H , T )$ and the damping of magnons due to classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the magnon spectrum is gapless when the spin rotational invariance is spontaneously broken, we use a Ward identity to express the magnon self-energy in terms of the magnetization. In two dimensions our approach correctly predicts the absence of long-range magnetic order for $H=0$ at finite temperature $T$. The magnon spectrum then exhibits a gap from which we obtain the transverse correlation length. We also calculate the wave-function renormalization factor of the magnons. As a mathematical by-product, we derive a recursive form of the generalized Wick theorem for spin operators in frequency space which facilitates the calculation of arbitrary time-ordered connected correlation functions of an isolated spin in a magnetic field.

cond-mat.stat-mech↗

arXiv2018

Exact renormalization group for quantum spin systems

We show that the diagrammatic approach to quantum spin systems developed in a seminal work by Vaks, Larkin, and Pikin [Sov. Phys. JETP 26, 188 (1968)] can be embedded in the framework of the functional renormalization group. The crucial insight is that the generating functional of the time-ordered connected spin correlation functions of an arbitrary quantum spin system satisfies an exact renormalization group flow equation which resembles the corresponding flow equation of a system of interacting bosons. The $SU (2)$ spin algebra is implemented via a non-trivial initial condition for the renormalization group flow. Our method is rather general and offers a new non-perturbative approach to quantum spin systems.

cond-mat.str-el↗

arXiv2018

A rich man's derivation of scaling laws for the Kondo model

We show how the one-loop "poor man's scaling" equations for the Kondo model with arbitrary impurity spin can be obtained within the framework of the functional renormalization group approach for quantum spin systems recently developed by Krieg and Kopietz [arXiv:1807.02524]. We argue that our method supersedes the "poor man's scaling" approach and can also be used to study the strong coupling regime of the Kondo model.

cond-mat.str-el↗

arXiv2018

Renormalization group for the $φ^4$-theory with long-range interaction and the critical exponent $η$ of the Ising model

We calculate the critical exponent $η$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the smallness of the inverse range of the interaction and on the assumption that the Ginzburg momentum defining the width of the scaling regime in momentum space is larger than the scale where the renormalized interaction crosses over from long-range to short-range; the numerical value of $η$ can then be estimated by stopping the renormalization group flow at this scale. In three dimensions our result $η= 0.03651$ is in good agreement with recent conformal bootstrap and Monte Carlo calculations. We extend our calculations to fractional dimensions $D$ and obtain the resulting critical exponent $η(D)$ between two and four dimensions. For dimensions $2\leq D \leq 3$ our result for $η$ is consistent with previous calculations.

cond-mat.stat-mech↗

arXiv2018

Functional renormalization group approach to interacting three-dimensional Weyl semimetals

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes --- cutoff in fermionic or bosonic propagators --- in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavski{ĭ} [Sov. Phys. JETP \textbf{32}, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

cond-mat.str-el↗

arXiv2017

Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations

We develop a new functional renormalization group (FRG) approach for the two-dimensional XY-model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation which explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

cond-mat.stat-mech↗

arXiv2017

Critical pairing fluctuations in the normal state of a superconductor: pseudogap and quasi-particle damping

We study the effect of critical pairing fluctuations on the electronic properties in the normal state of a clean superconductor in three dimensions. Using a functional renormalization group approach to take the non-Gaussian nature of critical fluctuations into account, we show microscopically that in the BCS regime, where the inverse coherence length is much smaller than the Fermi wavevector, critical pairing fluctuations give rise to a non-analytic contribution to the quasi-particle damping of order $ T_c \sqrt{Gi} \ln ( 80 / Gi )$, where the Ginzburg-Levanyuk number $Gi$ is a dimensionless measure for the width of the critical region. As a consequence, there is a temperature window above $T_c$ where the quasiparticle damping due to critical pairing fluctuations can be larger than the usual $T^2$-Fermi liquid damping due to non-critical scattering processes. On the other hand, in the strong coupling regime where $Gi$ is of order unity, we find that the quasiparticle damping due to critical pairing fluctuations is proportional to the temperature. Moreover, we show that in the vicinity of the critical temperature $T_c$ the electronic density of states exhibits a fluctuation-induced pseudogap. We also use functional renormalization group methods to derive and classify various types of processes induced by the pairing interaction in Fermi systems close to the superconducting instability.

cond-mat.supr-con↗

arXiv2017

Spin currents, spin torques, and the concept of spin superfluidity

In magnets with non-collinear spin configuration the expectation value of the conventionally defined spin current operator contains a contribution which renormalizes an external magnetic field and hence affects only the precessional motion of the spin polarization. This term, which has been named angular spin current by Sun and Xie [Phys. Rev B 72, 245305 (2005)], does not describe the translational motion of magnetic moments. We give a prescription how to separate these two types of spin transport and show that the translational movement of the spin is always polarized along the direction of the local magnetization. We also show that at vanishing temperature the classical magnetic order parameter in magnetic insulators cannot carry a translational spin current, and elucidate how this affects the interpretation of spin supercurrents.

cond-mat.mes-hall↗

arXiv2017

Thermodynamics and renormalized quasi-particles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wavefunction renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $μ$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization group calculations for thermodynamic observables at $μ=0$ to finite values of $μ$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, the susceptibility, and the correlation length of the two-dimensional spin-$1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $μ\leq 0$ rather accurately up to relatively high temperatures $T \lesssim 0.1 J$.

cond-mat.quant-gas↗

arXiv2016

Multilogarithmic velocity renormalization in graphene

We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene. Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff scheme, we calculate the quasiparticle velocity, $v (k)$, and the quasiparticle residue, $Z$, with frequency-dependent polarization. One of our most striking results is that $v ( k ) \propto \ln [ C_k (α) / k ]$ where the momentum- and interaction-dependent cutoff scale $C_k (α) $ vanishes logarithmically for $k \rightarrow 0$. Here $k$ is measured with respect to one of the charge neutrality (Dirac) points and $α=2.2$ is the strength of dimensionless bare interaction. Moreover, we also demonstrate that the so-obtained multilogarithmic singularity is reconcilable with the perturbative expansion of $v (k)$ in powers of the bare interaction.

cond-mat.str-el↗

arXiv2016

Physical dipoles and second order perturbation theory for dipolar fermions in two dimensions

In two dimensions the Fourier transform of the interaction between two point dipoles has a term which grows linearly in the modulus $| \mathbf{\textit{q}} |$ of the momentum . As a consequence, in second order perturbation theory the self-energy of two-dimensional dipolar fermions is ultraviolet divergent. We show that for electric dipoles this divergence can be avoided if one takes into account that physical dipoles consist of two opposite charges which are separated by a finite distance. Using this regularization, we calculate the self-energy, the renormalized chemical potential, and the renormalized Fermi surface of dipolar fermions in two dimensions in second order perturbation theory. We find that in the Fermi liquid phase the second order corrections weaken first order effects.

cond-mat.quant-gas↗

arXiv2015

Rayleigh-Jeans condensation of pumped magnons in thin film ferromagnets

We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with experiments. Our calculation proves that the experimentally observed condensation of magnons in yttrium-iron garnet at room temperature is a purely classical phenomenon which should be called Rayleigh-Jeans rather than Bose-Einstein condensation.

cond-mat.mes-hall↗

arXiv2015

Hard-core boson approach to the spin-1/2 triangular-lattice antiferromagnet Cs$_2$CuCl$_4$ at finite temperatures in magnetic fields higher than the saturation field

We study the high magnetic field regime of the antiferromagnetic insulator Cs$_2$CuCl$_4$ by expressing the spin-1/2 operators in the relevant Heisenberg model in terms of hard-core bosons and implementing the hard-core constraint via an infinite on-site interaction. We focus on the case where the external magnetic field exceeds the saturation field $B_{c}\approx8.5\;\mathrm{T}$ and is oriented along the crystallographic $a$ axis perpendicular to the lattice plane. Because in this case the excited states are separated by an energy gap from the ground state, we may use the self-consistent ladder approximation to take the strong correlations due to the hard-core constraint into account. In Cs$_2$CuCl$_4$ there are additional interactions besides the hard-core interaction which we treat in self-consistent Hartree-Fock approximation. We calculate the spectral function of the hard-core bosons from which we obtain the in-plane components of the dynamic structure factor, the magnetic susceptibility, and the specific heat. Our results for the specific heat are in good agreement with the available experimental data. We conclude that the self-consistent ladder approximation in combination with a self-consistent Hartree-Fock decoupling of the non-hard-core interactions gives an accurate description of the physical properties of gapped hard-core bosons in two dimensions at finite temperatures.

cond-mat.str-el↗