Abstract
We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.
Highlights
A number of strongly correlated materials with a metallic parent state exhibit a variety of non-Fermi-liquid (NFL) properties
In addition to the low-temperature Fermi-liquid and the high-temperature incoherent regime, we find an intermediate range of temperatures where the correlations in the narrow band are locally quantum critical, while the band with the larger bandwidth forms a marginal Fermi liquid, with a single-particle inverse lifetime proportional to maxðε; TÞ, where ε is the energy
On the basis of our study of all the models with locally critical d.o.f., we propose some general constraints on models with local quantum criticality in Sec
Summary
A number of strongly correlated materials with a metallic parent state exhibit a variety of non-Fermi-liquid (NFL) properties. The ground state is a Landau Fermi liquid or some other conventional state (e.g., a superconductor) and the strange metal regime appears only as a crossover at higher temperatures Despite all this progress in the theory of non-Fermi liquids, there is no clear mechanism that produces a linearin-T resistivity over a broad range of temperatures in quantum-critical or other non-Fermi liquids in translationally invariant models as a result of strong local electronic interactions. The appropriate description of a maximally chaotic bubble in such a metal will not likely be a SYK-like model and will, in the future, have to be replaced by a better theory that takes into account spatial locality within each bubble These solvable models point to the importance of maximally chaotic intermediate scale bubbles as a possible universal route to a class of non-Fermi liquids. A number of accompanying technical details appear in the appendixes
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