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The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-$N$ electron-phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits resistivity saturation to a temperature-independent value of the order of the quantum of resistivity - the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological parallel resistor formula, known to describe the resistivity of a variety of saturating metals.
One-electron self-energy in the $t$-$J$ model was computed using a recently developed large-$N$ method based on the path integral representation for Hubbard operators. One of the main features of the self-energy is its strong asymmetry with respect t
Significant effort has been devoted to the study of non-Fermi liquid (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter f
Resistivities of heavy-fermion insulators typically saturate below a characteristic temperature $T^*$. For some, metallic surface states, potentially from a non-trivial bulk topology, are a likely source of residual conduction. Here, we establish an
Large-$S$ and large-$N$ theories (spin value $S$ and spinor component number $N$) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-$S$ spin-wave theory captures the correct semiclassical behavior, large-$N$ t
We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed