Quantum Acoustics Demystifies the Strange Metals

TL;DR

This work reframes lattice vibrations in solids as a time-dependent, nonperturbative vibronic medium within a coherent-state (quantum acoustics) framework, unifying waves and particles through the wave-on-wave (WoW) approach. By treating the deformation potential dynamically and back-action with exact path-integral and stochastic methods, the authors derive Planckian diffusion with a diffusion constant $D\approx \hbar/m^*$, yielding linear-in-$T$ resistivity and bypassing the MIR limit in strange metals. The theory naturally explains polaron and charge-density-wave formation, Drude-peak displacement in optics, and the apparent isotropy of scattering rates, offering a common microscopic origin for diverse strange-metal phenomena anchored in the Fröhlich model. The results imply a universal, diffusion-dominated transport regime driven by vibronic coupling, with broad implications for interpreting transport in high-$T_c$ materials and other dynamic disordered media.

Abstract

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 $T^4$ 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''.

Figures (15)

• Figure 1: Photocopy from Schrödinger's 1926 paper, showing his drawing of what we now call a coherent state of the harmonic oscillator. In the present context, second quantized number states lie on the left, and coherent states on the right. They do not cancel out each other's "new physics".
• Figure 2: A snapshot of the deformation potential in colorscale after a polaron had recently formed about 3 psec into the WoW propagation. This is a good moment to herald the power of the coherent state representation: The entire scene seen in figure \ref{['polaron3psec']}, including the polaron and waves emanating from it, and the thermal part of the deformation potential, plus information hidden in the snapshots about the rate of change of all these things, is provided by a single multivariate Gaussian coherent state. All that complexity is contained in one coherent state configuration.
• Figure 3: Four wave-particle dualities of crystal lattice quantum mechanics. Reading across in the top row, the Fock $\vert n_{\vec{q}}\rangle$ state particle representation (left) corresponds to a wave in the corresponding $\vec{q}$ normal mode (right). In the lower row, a real space vibrational wave pattern, (left) lives on the lattice, in which the atoms are all given quite well-defined positions and momenta (within the uncertainty principle). This corresponds to a coherent state particle, right, a compact coherent state. Reading down, two more dualities emerge. In the left column, there is a duality regarding the lattice, with a particle representation at the top, and waves below. In the right column, there is a duality regarding the modes, and we go from a wave at the top, to wavepacket particles below.
• Figure 4: Particles and waves in quantum optics and quantum acoustics. Electrons interact with the photons, or vacuum light waves on the left, or phonons, or lattice sound waves on the right.
• Figure 5: At the top, a perturbative Compton scattering picture is characteristic of 70 years of solid state theory, carefully balancing energy and momentum in a local process. Bereft of any easy extension beyond first order, incoherent Boltzmann transport in assumed in order to get to go to higher order in an ersatz way. This is Bloch-Grüneisen theory, which works well for ordinary metals. Below, total energy and momentum, field plus particle, are not nearly so carefully balanced, as when an electron deflects in an electromagnetic field for example. Behind the scenes, of course both are conserved. What is shown is a time dependent quantum electron wave navigating a random thermal, blackbody-like sea of the lattice deformation potential. In our work, the electron and lattice exchange energy and momentum via mean field back-action. While this neglects quantum entanglements that develop, this is much less of a sin than throwing coherence out altogether beyond first order.