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arXiv:2106.04479 · Physical review. B./Physical review. B

Transport in the two-dimensional Fermi-Hubbard model: Lessons from weak coupling

Thomas G. Kiely, Erich J. Mueller

Published Oct 25, 2021• 13 citations
arXivHTMLPDF

Abstract

Strongly correlated materials, where electron-electron interactions dominate, display a range of important yet poorly understood phenomena including high-temperature superconductivity and exotic magnetism. Many such materials also feature unusual ``strange-metal'' transport, corresponding to unexpected temperature dependence of the resistivity. The authors show that, due to band-structure nesting and a bounded spectrum, even a weakly interacting system can display resistivity signatures that are typically associated with such strange metals. Their results are particularly important for interpreting recent cold-atom experiments which explore transport in the Fermi Hubbard model.

DOI
10.1103/physrevb.104.165143

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Strongly correlated materials, where electron-electron interactions dominate, display a range of important yet poorly understood phenomena including high-temperature superconductivity and exotic magnetism. Many such materials also feature unusual ``strange-metal'' transport, corresponding to unexpected temperature dependence of the resistivity. The authors show that, due to band-structure nesting and a bounded spectrum, even a weakly interacting system can display resistivity signatures that are typically associated with such strange metals. Their results are particularly important for interpreting recent cold-atom experiments which explore transport in the Fermi Hubbard model.
Recent cold atom experiments have observed bad and strange metal behaviors in strongly-interacting Fermi-Hubbard systems. Motivated by these results, we calculate the thermoelectric transport properties of a 2D Fermi-Hubbard system in the weak coupling limit using quantum kinetic theory. We find that many features attributed to strong correlations are also found at weak coupling. In particular, for temperatures T≳tT\gtrsim tT≳t the electrical resistivity is nearly linear in temperature despite the fact that the quasiparticle scattering rate is non-linear and changes by nearly an order of magnitude. We argue that this asymptotic behavior is a general feature of systems with a finite spectral width, which implies that there is no MIR bound on the resistivity in single-band models. Due to nesting, the TTT-linear resistivity persists down to T=0T=0T=0 at half filling. Our work sheds light on the transport regime in ultracold atom experiments, which can differ substantially from that of condensed matter systems. Disentangling these band-structure effects from the physics of strong correlations is a major challenge for future experiments.
Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.
Correlated Electrons In many materials, charge carriers are well described as noninteracting quasiparticles. However, in materials with strong correlations, this approximation can break down, leading to anomalous transport properties at high temperatures. Huang et al. used quantum Monte Carlo calculations to look for this so-called strange metal phase in the simplest two-dimensional model of interacting electrons, the Hubbard model. They found that the calculated resistivity had a linear temperature dependence when hole doping was introduced, as expected in the strange metal phase. This observation provides confidence that simplified models can be used to describe and understand the behavior of real materials, such as cuprate high-temperature superconductors. Science , this issue p. [987][1] [1]: /lookup/doi/10.1126/science.aau7063
Non-saturating high-temperature resistivity ("bad metal"), T-linear low-temperature resistivity ("strange metal"), and a crossover to activation-free growth of the resistivity in the low-temperature limit ("weak insulator") are among the most exotic behaviors widely observed in many strongly correlated materials for decades that defy the standard Fermi liquid description of solids. Here we investigate these puzzling behaviors by computing temperature-dependent optical conductivity of an emergent Bose liquid and find that it reproduces all the unexplained features of the experiments, including a featureless continuum and a well-known mid-infrared peak. Amazingly and with physically intuitive mechanisms, the corresponding doping- and temperature-dependent resistivity displays the bad metal and strange metal simultaneously and sometimes weak insulating behaviors as well. The unification of all these non-Fermi liquid behaviors in a single model suggests that a new quantum state of matter, namely the emergent Bose liquid, will guide the development of the next generation of solid state physics.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via Z2{Z}_{2}Z2​ antiferromagnetic quantum critical fluctuations by means of a sign-problem-free quantum Monte Carlo approach. We show that the phase diagram of this model indeed contains a ddd-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above Tc{T}_{c}Tc​, exhibiting hallmark strange-metal transport phenomenology. Interestingly, we find that this version of the model describes a non-Fermi-liquid metallic regime that displays an approximately TTT-linear resistivity above Tc{T}_{c}Tc​ for a strong fermion-boson interaction. Using the Nernst-Einstein relation, our QMC results also show that this strange metal phase exhibits a crossover from being characterized by a charge compressibility given approximately by ${\ensuremath{\chi}}_{c}\ensuremath{\sim}1/T$ at high temperatures to being described by a charge diffusivity consistent with the scaling ${D}_{c}\ensuremath{\sim}1/T$ at low temperatures. Therefore, our paper adds support to the view that the Z2{Z}_{2}Z2​ antiferromagnetic spin-fermion model at strong coupling can be considered a minimal model that describes both unconventional superconductivity and strange metallicity, which are fundamentally interconnected in many important strongly correlated quantum materials.
“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ( T ) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large- N limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in- T resistivity with a universal “Planckian” transport scattering rate Γ tr ∼ k B T / ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.