Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van Hove singularity of the electronic spectrum crosses the Fermi energy, is expected to cause a change in the temperature dependence of the electrical resistivity from its Fermi l
iquid behavior $rhosim T^{2}$ to $rhosim T^{2}{rm log}left(1/Tright)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation originates from the same multi-band scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the strange metal Sr$_{3}$Ru$_{2}$O$_{7}$. In contrast, the thermal resistivity $rho_{Q}equiv T/kappa$, where $kappa$ is the thermal conductivity, is governed by qualitatively distinct processes that involve a broad continuum of compressive modes, i.e. long wavelength density excitations in Van Hove systems. While these compressive modes do not affect the charge current, they couple to thermal transport and yield $rho_{Q}propto T^{3/2}$. As a result, we predict that the Wiedemann-Franz law in strained Sr$_{2}$RuO$_{4}$ should be violated with a Lorenz ratio $Lpropto T^{1/2}{rm log}left(1/Tright)$. We expect this effect to be observable in the temperature and strain regime where the anomalous charge transport was established.
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.
In this work we consider the hydrodynamic behavior of a coupled electron-phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scatterin
g is much slower than the rate of normal electron-phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron-phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker-Planck approximation, applied to the electron-phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron-phonon drag measurements in Dirac and Weyl semimetals.
We determine the information scrambling rate $lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $lambda_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic trans
port coefficients of a many-body system. We demonstrate that $lambda_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $lambda_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.
In this paper we study the critical behavior of an $N$-component ${phi}^{4}$-model in hyperbolic space, which serves as a model of uniform frustration. We find that this model exhibits a second-order phase transition with an unusual magnetization tex
ture that results from the lack of global parallelism in hyperbolic space. Angular defects occur on length scales comparable to the radius of curvature. This phase transition is governed by a new strong curvature fixed point that obeys scaling below the upper critical dimension $d_{uc}=4$. The exponents of this fixed point are given by the leading order terms of the $1/N$ expansion. In distinction to flat space no order $1/N$ corrections occur. We conclude that the description of many-particle systems in hyperbolic space is a promising avenue to investigate uniform frustration and non-trivial critical behavior within one theoretical approach.
We analyze whether and how the neutron resonance mode in unconventional superconductors is affected by higher order corrections in the coupling between spin excitations and fermionic quasiparticles and find that in general such corrections cannot be
ignored. In particular, we find that in two spatial dimensions (d=2) the corrections are of same order as the leading, weak coupling contributions demonstrating that the neutron resonance mode in unconventional superconductors is a strong coupling phenomenon. The origin of this behavior lies in the quantum-critical nature of the low energy spin dynamics in the superconducting state and the feedback of the resonance mode onto the fermionic excitations. While quantum critical fluctuations occur in any dimensionality smaller than the upper critical dimension d_{uc}=3, they can be analyzed in a controlled fashion by means of the epsilon-expansion (epsilon =3-d), such that the leading corrections to the resonance mode position are small. Regardless of the strong coupling nature of the resonance mode we show that it emerges only if the phase of the superconducting gap function varies on the Fermi surface, making it a powerful tool to investigate the microscopic structure of the pair condensate.
