Understanding transport of charge excitations in strongly correlated electron systems exhibiting the ``strange metal'' state without long-lived quasiparticle excitations has been a long-standing challenge in condensed matter physics. Here, the authors demonstrate that thermal diffusivity, which tracks energy-thermalization processes, exhibits a limiting Planckian relaxation time and a unique thermal diffusion velocity. These reflect both the contribution of phonons and electrons. This result is bound by the thermal diffusivity of the electrons at the Mott-Ioffe-Regel limit, where the mean-free-path reaches atomic distances.
Understanding transport of charge excitations in strongly correlated electron systems exhibiting the ``strange metal'' state without long-lived quasiparticle excitations has been a long-standing challenge in condensed matter physics. Here, the authors demonstrate that thermal diffusivity, which tracks energy-thermalization processes, exhibits a limiting Planckian relaxation time and a unique thermal diffusion velocity. These reflect both the contribution of phonons and electrons. This result is bound by the thermal diffusivity of the electrons at the Mott-Ioffe-Regel limit, where the mean-free-path reaches atomic distances.
We calculate the scrambling rate λL and the butterfly velocity vB associated with the growth of quantum chaos for a solvable large-N electron-phonon system. We study a temperature regime in which the electrical resistivity of this system exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles. The long-lived phonons determine λL, rendering it parametrically smaller than the theoretical upper-bound λL≪λmax=2πT/ℏ. Significantly, the chaos properties seem to be intrinsic - λL and vB are the same for electronic and phononic operators. We consider two models - one in which the phonons are dispersive, and one in which they are dispersionless. In either case, we find that λL is proportional to the inverse phonon lifetime, and vB is proportional to the effective phonon velocity. The thermal and chaos diffusion constants, DE and DL≡vB2/λL, are always comparable, DE∼DL. In the dispersive phonon case, the charge diffusion constant DC satisfies DL≫DC, while in the dispersionless case DL≪DC.
Phonons have long been thought to be incapable of explaining key phenomena in strange metals, including linear-in-\textit{T} Planckian resistivity from high to very low temperatures. We argue that these conclusions were based on static, perturbative approaches that overlooked essential time-dependent and nonperturbative electron-lattice physics. In fact ``phonons'' are not the best target for discussion, just like ``photons'' are not the best way to think about Maxwell's equations. Quantum optics connects photons and electromagnetism, as developed 60 years ago by Glauber and others. We have been developing the parallel world of quantum acoustics. Far from being only of academic interest, the new tools are rapidly exposing the secrets of the strange metals, revealing strong vibronic (vibration-electronic) interactions playing a crucial role forming polarons and charge density waves, linear-in-T resistivity at the Planckian rate over thousands of degrees, resolution of the Drude peak infrared anomaly, and the absence of a T4 low-temperature resistivity rise in 2D systems, and of a Mott-Ioffe-Regel resistivity saturation. We derive Planckian transport, polarons, CDWs, and pseudogaps from the Fröhlich model. The ``new physics'' has been hiding in this model all along, in the right parameter regime, if it is treated nonperturbatively. In the course of this work we have uncovered the generalization of Anderson localization to dynamic media: a universal Planckian diffusion emerges, a ``ghost'' of Anderson localization. Planckian diffusion is clearly defined and is more fundamental than the popular but elusive, model dependent concept of ``Planckian speed limit''.
Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.
I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit D=ℏ/m, and that such quantum carriers behave as distinguishable particles as they would in an electronic solid. These assumptions immediately lead to T-linear resistivities with apparent Planckian scattering rates and, extending to the frequency domain, to the stretched Drude peaks and ω/T scaling commonly observed in optical absorption experiments in strange metals. This behavior can be rationalized by observing that when the thermal de Broglie length λ_{dB} exceeds the mean-free path, the carrier motion can no longer be described in terms of random collisions of classical particles as assumed by Drude-Boltzmann theory and should be viewed instead as a sequence of projective measurements collapsing the wave function.
Good metals are characterized by diffusive transport of coherent quasiparticle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, e2ha, where a is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge-diffusion constant, $D\ensuremath{\gtrsim}\ensuremath{\hbar}{v}_{F}^{2}/({k}_{B}T)$, in the incoherent regime of transport, where vF is the Fermi velocity and T the temperature. Using dynamical mean-field theory (DMFT) we calculate the charge-diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi-liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity vF is replaced by its low-temperature renormalized value vF∗. The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high-temperature region where the resistivity is close to linear in temperature. Our calculated charge-diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, ${D}_{s}\ensuremath{\sim}1.3\ensuremath{\hbar}/m$, where m is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.
A key challenge for optical lattice experiments focused on simulating models of strongly correlated electronic solids has been achieving lower temperatures. Although cooling of lattice-well vibrational states has been demonstrated, the motion of atoms through the lattice, characterized by their quasimomentum, has not been cooled directly. Furthermore, quasimomentum equilibration, which is necessary for cooling, has remained unexplored. Here, we use quasimomentum-selective stimulated Raman transitions to directly measure rethermalization rates and cool quasimomentum for a bosonic lattice Hubbard gas. The measured relaxation rate is consistent with a short-range, two-particle scattering model without free parameters at high lattice depths, despite an apparent violation of the Mott-Ioffe-Regel (MIR) bound. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides, and the cooling method we have developed is applicable to any species, including fermionic atoms.