arXiv subjects

Peter Kopietz

Publications and source records attributed to Peter Kopietz.

At least 19 recordsLinked to original sources

arXiv2026

Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet

Using an extension of the fermionic functional renormalization group for systems where strong correlations give rise to projected Hilbert spaces we calculate the phase diagram and the electronic spectral function of the Hubbard model at infinite on-site repulsion. For a square lattice with nearest-neighbor hopping we find that the ground state evolves from a paramagnetic Fermi liquid at low densities via a state with antiferromagnetic stripe order at intermediate densities to an extended Nagaoka ferromagnet at high densities. The single-particle spectral function of the Nagaoka ferromagnet exhibits a flat but rather broad band characteristic for an incoherent non-Fermi liquid. We identify two distinct ferromagnetic regimes separated by a Lifshitz transition.

cond-mat.str-el↗

arXiv2026

Functional renormalization group for extremely correlated electrons

At strong on-site repulsion $ U $, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict $ U = \infty $ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger's theorem.

cond-mat.str-el↗

arXiv2026

Fermion condensation in a generalized Hatsugai-Kohmoto model with momentum-mixing Landau interactions

The Hatsugai-Kohmoto (HK) model is an exactly solvable electronic lattice model where the interaction between electrons with opposite spin is diagonal in momentum space. We generalize the HK model by introducing momentum-mixing Landau interactions. Within a self-consistent mean-field analysis we find that the ground state of this model exhibits a partially flat energy band, in agreement with the fermion condensation scenario proposed by Khodel and Shaginyan [JETP Lett. 51, 553 (1990)]. Inspired by Andersons pseudospin formulation of BCS theory, we show that the HK model with Landau interactions can be mapped onto a generalized Ising model where each site of the reciprocal lattice hosts two Ising spins. In the pseudospin picture the emergence of a partially flat electronic band corresponds to the smoothing of a magnetic domain wall. Moreover, guided by the pseudospin picture, we propose an exactly solvable variant of the HK model which has a unique ground state for all densities.

cond-mat.str-el↗

arXiv2025

Spontaneous magnon decay in two-dimensional altermagnets

We show that magnons in two-dimensional altermagnets can spontaneously decay at zero temperature. The decay rate is determined by quantum fluctuations and scattering processes involving the decay of a single magnon into three. These processes are kinematically allowed due to the convexity of the altermagnetic magnon dispersion. For small wavevectors $k$ the decay rate is proportional to $k^5$ with a direction-dependent prefactor which is maximal along the diagonals of the Brillouin zone. Moreover, for a given momentum only magnons with one specific chirality can spontaneously decay.

cond-mat.str-el↗

arXiv2025

Quantum fluctuations in two-dimensional altermagnets

The magnetic properties of two-dimensional altermagnets can be obtained from a square lattice Heisenberg model with antiferromagetic nearest neighbor interaction and two types of next-nearest neighbor interactions arranged in a checkerboard pattern. Using nonlinear spin-wave theory we calculate for this model the corrections to the renormalized magnon spectrum and the staggered magnetization to first order in the inverse spin quantum number $1/S$. We also show that to order $1/S^2$ the ground state energy is not sensitive to the component of the interaction which is responsible for altermagnetism. At the $Γ$-point the $1/S$-correction to the magnon dispersion vanishes so that quantum fluctuations do not induce a gap in the magnon spectrum of altermagnets, as expected by Goldstone's theorem. We extract the leading $1/S$-corrections to the spin-wave velocity and the effective mass characterizing the curvature of the magnon dispersion in altermagnets.

cond-mat.str-el↗

arXiv2025

Functional renormalization group approach to phonon modified criticality: anomalous dimension of strain and non-analytic corrections to Hooke's law

We study the interplay between critical isotropic elasticity and classical Ising criticality using a functional renormalization group (FRG) approach which is implemented such that the volume is fixed during the entire renormalization group flow. For dimensions slightly smaller than four we use a simple truncation of the FRG flow equations to recover the fixed points of the constrained Ising model: the Gaussian fixed point G, the Ising fixed point I, the renormalized Ising fixed point R, and the spherical fixed point S. We show that the fixed points R and S are both characterized by a finite anomalous dimension $y_{\ast}<0$ of strain fluctuations, implying that the energy dispersion of longitudinal acoustic phonons exhibits a non-analytic momentum dependence proportional to $k^{1-y_{\ast}/2}$ for small momentum $k$. We also derive and solve flow equations for the free energy at constant strain and compute stress-strain relations in the vicinity of the fixed points. As a result, we reaffirm that Ising criticality, controlled by the fixed point I, is preempted by a bulk instability. Beyond that, we find that the stress-strain relation at R and S remains linear to leading order (Hooke's law), as long as the interaction between strain and Ising fluctuations is sufficiently weak. However, the finite anomalous dimension of strain fluctuations $y_{\ast}$ gives rise to non-analytic corrections to Hooke's law.

cond-mat.stat-mech↗

arXiv2025

Plasmon-sound hybridization in ionic crystals

We study the hybridization between plasmons, phonons, and electronic sound in ionic crystals using the Debye model, where the ionic background is modeled as a homogeneous, isotropic, elastic medium. We explicitly obtain the energies and the damping of the hybrid plasmon-sound modes in the hydrodynamic regime and calculate the corresponding dynamic structure factor. We find that with increasing viscosity a plasmon-like mode quickly decays into a broad, incoherent background, while a phonon-like mode with linear dispersion remains rather sharp. The quantitative behavior of the hybridized collective modes depends on the ratio of the electronic and the ionic plasma frequencies. We also show that the direct Coulomb interaction between the ions is essential to obtain a collective sound mode with linear dispersion.

cond-mat.str-el↗

arXiv2024

Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility

We show that the high-temperature expansion of the free energy and arbitrary imaginary-time-ordered connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly written down in closed form including all combinatorial factors. We use our method to estimate critical temperatures of Heisenberg magnets from low-order truncations of the inverse spin susceptibility in the static limit. We also calculate the connected correlation function involving three different spin components (chiral non-linear susceptibility) of quantum Heisenberg magnets up to second order in the exchange couplings.

cond-mat.str-el↗

arXiv2024

Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin

We use the spin functional renormalization group to investigate the $J_1$-$J_2$ quantum Heisenberg model on a square lattice. By incorporating sum rules associated with the fixed length of the spin operators as well as the nontrivial quantum dynamics implied by the spin algebra, we are able to compute the ground state phase diagram for arbitrary spin $S$, including the quantum paramagnetic phase at strong frustration. Our prediction for the extent of this paramagnetic region for $ S = 1/2 $ agrees well with other approaches that are computationally more expensive. We find that the quantum paramagnetic phase disappears for $ S \gtrsim 5 $ due to the suppression of quantum fluctuations with increasing $S$.

cond-mat.str-el↗

arXiv2024

Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model

Using a functional renormalization group approach we derive the renormalization group (RG) flow of a dissipative variant of the Yukawa-Sachdev-Ye-Kitaev model describing $N$ fermions on a quantum dot which interact via a disorder-induced Yukawa coupling with $M$ bosons. The inverse Euclidean propagator of the bosons is assumed to exhibit a non-analytic term proportional to the modulus of the Matsubara frequency. We show that, to leading order in $1/N$ and $1/M$, the hierarchy of formally exact flow equations for the irreducible vertices of the disorder-averaged model can be closed at the level of the two-point vertices. We find that the RG flow exhibits a non-Fermi liquid fixed point characterized by a finite fermionic anomalous dimension $η$ which is related to the bosonic anomalous dimension $γ$ via the scaling law $2 = 2 η+ γ$ with $ 0 < η< 1/2$. We explicitly calculate $η$ and the critical exponents characterizing the linearized RG flow in the vicinity of the fixed point as functions of $N/M$.

cond-mat.str-el↗

arXiv2023

Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators

Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to models for strongly correlated electrons with projected Hilbert spaces, such as quantum spin models, the $t$-$J$ model, or the Hubbard model at infinite on-site repulsion. By representing these models in terms of Hubbard X-operators, we derive exact flow equations for the time-ordered correlation functions of the X-operators (X-FRG), which allow us to calculate the electronic correlation functions in the projected Hilbert space of these models. The Hubbard-I approximation for the single-particle Green function of the Hubbard model is recovered from a trivial truncation of the flow equations where the two-point vertex is approximated by its atomic limit. We use our approach to calculate the quasi-particle residue and damping in the ``hidden Fermi liquid'' state of the Hubbard model at infinite on-site repulsion where the Hamiltonian consists only of the projected kinetic energy.

cond-mat.str-el↗

arXiv2023

Collective modes in the charge-density wave state of K$_{0.3}$MoO$_3$: The role of long-range Coulomb interactions revisited

We re-examine the effect of long-range Coulomb interactions on the collective amplitude and phase modes in the incommensurate charge-density-wave ground state of quasi-one-dimensional conductors. Using an effective action approach we show that the longitudinal acoustic phonon protects the gapless linear dispersion of the lowest phase mode in the presence of long-range Coulomb interactions. Moreover, in Gaussian approximation, amplitude fluctuations are not affected by long-range Coulomb interactions. We also calculate the collective mode dispersions at finite temperatures and compare our results with the measured energies of amplitude and phase modes in K$_{0.3}$MoO$_3$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multi-phonon Fröhlich model for generic electron-phonon interactions neglecting long-range Coulomb interactions.

cond-mat.str-el↗

arXiv2023

Spin functional renormalization group for the $J_{1}J_{2}J_{3}$ quantum Heisenberg model

We use our recently developed functional renormalization group (FRG) approach for quantum spin systems to investigate the phase diagram of the frustrated $J_{1}J_{2}J_{3}$ quantum Heisenberg model on a cubic lattice. From a simple truncation of the hierarchy of FRG flow equations for the irreducible spin-vertices which retains only static spin fluctuations and neglects the flow of the four-spin interaction, we can estimate the critical temperature with a similar accuracy as the numerically more expensive pseudofermion FRG. In the regime where the ground state exhibits either ferromagnetic or antiferromagnetic order, a more sophisticated truncation including the renormalization of the four-spin interaction as well as dynamic spin fluctuations reveals the underlying renormalization group fixed point and yields critical temperatures which deviate from the accepted values by at most 4 %.

cond-mat.str-el↗

arXiv2022

Phonon renormalization and Pomeranchuk instability in the Holstein model

The Holstein model with dispersionless Einstein phonons is one of the simplest models describing electron-phonon interactions in condensed matter. A naive extrapolation of perturbation theory in powers of the relevant dimensionless electron-phonon coupling $λ_0$ suggests that at zero temperature the model exhibits a Pomeranchuk instability characterized by a divergent uniform compressibility at a critical value of $λ_0$ of order unity. In this work, we re-examine this problem using modern functional renormalization group (RG) methods. For dimensions $d > 3$ we find that the RG flow of the Holstein model indeed exhibits a tricritical fixed point associated with a Pomeranchuk instability. This non-Gaussian fixed point is ultraviolet stable and is closely related to the well-known ultraviolet stable fixed point of $ϕ^3$-theory above six dimensions. To realize the Pomeranchuk critical point in the Holstein model at fixed density both the electron-phonon coupling $λ_0$ and the adiabatic ratio $ω_0 / ε_F$ have to be fine-tuned to assume critical values of order unity, where $ω_0$ is the phonon frequency and $ε_F$ is the Fermi energy. On the other hand, for dimensions $d \leq 3$ we find that the RG flow of the Holstein model does not have any critical fixed points. This rules out a quantum critical point associated with a Pomeranchuk instability in $d \leq 3$.

cond-mat.str-el↗

arXiv2022

Spin functional renormalization group for dimerized quantum spin systems

We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)] which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean field critical exponents at the two quantum critical points.

cond-mat.str-el↗

arXiv2022

Accumulation of magnetoelastic bosons in yttrium iron garnet: kinetic theory and wave vector resolved Brillouin light scattering

We derive and solve quantum kinetic equations describing the accumulation of magnetoelastic bosons in an overpopulated magnon gas realized in a thin film of the magnetic insulator yttrium iron garnet. We show that in the presence of a magnon condensate, there is a non-equilibrium steady state in which incoherent magnetoelastic bosons accumulate in a narrow region in momentum space for energies slightly below the bottom of the magnon spectrum. The results of our calculations agree quite well with Brillouin light scattering measurements of the stationary non-equilibrium state of magnons and magnetoelastic bosons in yttrium iron garnet.

cond-mat.mes-hall↗

arXiv2022

Critical spin dynamics of Heisenberg ferromagnets revisited

We calculate the dynamic structure factor $S (\boldsymbol{k},ω)$ in the paramagnetic regime of quantum Heisenberg ferromagnets for temperatures $T$ close to the critical temperature $T_c$ using our recently developed functional renormalization group approach to quantum spin systems. In $d=3$ dimensions we find that for small momenta $\boldsymbol{k}$ and frequencies $ω$ the dynamic structure factor assumes the scaling form $S(\boldsymbol{k},ω) = (τT G (\boldsymbol{k})/π)Φ(kξ, ωτ)$, where $ G (\boldsymbol{k})$ is the static spin-spin correlation function, $ξ$ is the correlation length, and the characteristic time-scale $τ$ is proportional to $ξ^{5/2}$. We explicitly calculate the dynamic scaling function $Φ(x,y)$ and find satisfactory agreement with neutron scattering experiments probing the critical spin dynamics in EuO and EuS. Precisely at the critical point where $ξ= \infty$ our result for the dynamic structure factor can be written as $S (\boldsymbol{k},ω) = (πω_k)^{-1} T_c G (\boldsymbol{k}) Ψ_c (ω/ω_k)$, where $ω_k \propto k^{5/2}$. We find that $Ψ_c(ν)$ vanishes as $ν^{-13/5}$ for large $ν$, and as $ν^{3/5}$ for small $ν$. While the large-frequency behavior of $Ψ_c (ν)$ is consistent with calculations based on mode-coupling theory and with perturbative renormalization group calculations to second order in $ε= 6-d$, our result for small frequencies disagrees with previous calculations. We argue that up until now neither experiments nor numerical simulations are sufficiently accurate to determine the low-frequency behavior of $Ψ_c (ν)$. We also calculate the low-temperature behavior of $S ( \boldsymbol{k},ω)$ in one- and two dimensional ferromagnets and find that it satisfies dynamic scaling with exponent $z=2$ and exhibits a pseudogap for small frequencies.

cond-mat.stat-mech↗

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↗