Abstract
A theoretical understanding of the enigmatic linear-in-temperature (T) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust T-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub “slope invariance.” Recently, several solvable models with T-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate T linearity: a lattice of coupled Sachdev-Ye-Kitaev models and the Hubbard model in single-site dynamical mean-field theory. We find that the two models achieve T linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit “slope invariance” across the two temperature regimes. Thus not only do we reveal some of the diversity in the theoretical inner workings that can lead to T-linear resistivity, but we also establish that different mechanisms can result in “slope invarance.”Received 28 October 2019Revised 10 July 2020Accepted 16 July 2020Corrected 11 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033434Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectrical conductivityPhysical SystemsStrongly correlated systemsTechniquesDynamical mean field theoryHubbard modelNon-Fermi-liquid theorySachdev-Ye-Kitaev modelCondensed Matter & Materials Physics
Highlights
The mysterious incoherent metallic states with T -linear resistivity seen in many strongly correlated materials [1,2,3] have long puzzled researchers, as such a temperature dependence is inaccessible from Fermi liquid theory [4]
Remarkable is the fact that the slope dρDC/dT remains constant as T varies over two or three orders of magnitude, while the temperature shoots through multiple crossover energy scales: we dub this phenomenon “slope invariance.”
The unusual feature of local self-energy is at play in two of the most studied microscopic models with T -linear resistivity: lattice models of coupled Sachdev-Ye-Kitaev (SYK) quantum dots [5,6,7,8] and its earlier incarnation of a doped random-bond Heisenberg model [12] and the Hubbard model in single-site dynamical mean-field theory (DMFT) [11,13,14]
Summary
The mysterious incoherent metallic states with T -linear resistivity (ρDC ∝ T ) seen in many strongly correlated materials [1,2,3] have long puzzled researchers, as such a temperature dependence is inaccessible from Fermi liquid theory [4]. The unusual feature of local self-energy is at play in two of the most studied microscopic models with T -linear resistivity: lattice models of coupled Sachdev-Ye-Kitaev (SYK) quantum dots [5,6,7,8] and its earlier incarnation of a doped random-bond Heisenberg model [12] and the Hubbard model in single-site dynamical mean-field theory (DMFT) [11,13,14]. In both models, exact nontrivial self-consistency equations. T -linear resistivity arise from different functional forms of the spectral function
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