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."
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."
Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.
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 < ∞. 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.
Using determinant quantum Monte Carlo simulations, we compare charge transport in the two-dimensional attractive and repulsive Hubbard models at strong coupling, ∣U∣/t=6. Although the interaction with opposite signs generates qualitatively different low-energy spin, charge, and pairing correlations, both exhibit approximately linear-in-temperature resistivity over a broad intermediate- and high-temperature regime. At asymptotically high temperature this common behavior follows from the moment expansion of the conductivity, whose leading contribution is even in U. More strikingly, the similarity persists to temperatures well below ∣U∣, where strong interaction-dependent correlations have already developed, and also irrespective of whether resistivity crosses the MIR limit. Using the Nernst--Einstein relation, we find that the common linear-in-temperature resistivity is primarily associated with an approximately Curie-like charge compressibility and weakly temperature-dependent diffusivity. The two models separate only at lower temperatures, where the attractive model develops a pronounced feature in the charge diffusivity correlated with signatures of pair formation. These results show that linear-in-temperature incoherent transport in the Hubbard model can be remarkably insensitive to the microscopic nature of the low-energy correlations. Our results suggest that transport in the incoherent regime appears insensitive to what the system will ultimately become at low temperature; the distinction between competing low-energy states becomes visible only when their characteristic correlations acquire sufficiently long spatial or temporal coherence.
The description of the dynamics of strongly correlated quantum matter is a challenge, particularly in physical situations where a quasiparticle description is absent. In such situations, however, the many-body Kubo formula from linear response theory, involving matrix elements of the current operator computed with many-body wave functions, remains valid. Working directly in the many-body Hilbert space and not making any reference to quasiparticles (or lack thereof), we address the puzzle of linear in temperature (T-linear) resistivity seen in non-Fermi-liquid phases that occur in several strongly correlated condensed matter systems. We derive a simple criterion for the occurrence of T-linear resistivity based on an analysis of the contributions to the many-body Kubo formula, determined by an energy invariant ``f function'' involving current matrix elements and energy eigenvalues that describes the dc conductivity of the system in the microcanonical ensemble. Using full diagonalization, we test this criterion for the f function in the spinless nearest-neighbor Hubbard model and in a system of Sachdev-Ye-Kitaev dots coupled by weak single-particle hopping. We also study the f function for the spin conductivity in the two-dimensional Heisenberg model and arrive at similar conclusions. Our work suggests that a general principle, formulated in terms of many-body Hilbert space concepts, is at the core of the occurrence of T-linear resistivity in a wide range of systems, and precisely translates T-linear resistivity into a notion of energy scale invariance far beyond what is typically associated with quantum critical points.
In this paper, we present a theoretical framework for understanding the extremely correlated Fermi liquid (ECFL) phenomenon within the $U=\ensuremath{\infty}$ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function G and its associated self-energy $\mathrm{\ensuremath{\Sigma}}$, which involves the product of the bosonic correlation function comprising both density (DN) and spin (DS) correlations with G. By solving these equations self-consistently, we explore the behavior of G, DN, and DS as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity $\ensuremath{\rho}(T)$, observing a crossover from T2 to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and ``classical'' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.
In this paper, we present a theoretical framework for understanding the Extremely Correlated Fermi Liquid (ECFL) phenomenon within the U=∞ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function G and its associated self-energy Σ, which involves the product of the bosonic correlation function comprising both density (DN) and spin (DS) correlations with G. By solving these equations self-consistently, we explore the behavior of G, DN, and DS as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity ρ(T), observing a crossover from T2 to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and `classical' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.