“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.
“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.
Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.
Fermi liquid theory forms the basis for our understanding of the majority of metals, which is manifested in the description of transport properties that the electrical resistivity goes as temperature squared in the limit of zero temperature. However, the observations of strange metal states in various quantum materials, notably high-temperature superconductors, bring this spectacularly successful theoretical framework into crisis. When electron scattering rate 1/τ hits its limit, kBT/{\hbar} where {\hbar} is the reduced Planck's constant, T represents absolute temperature and kB denotes Boltzmann's constant, Planckian dissipation occurs and lends strange metals a surprising link to black holes, gravity, and quantum information theory. Here, we show the characteristic signature of strange metallicity arising unprecedentedly in a bosonic system. Our nanopatterned YBa2Cu3O7-δ(YBCO) film arrays reveal T-linear resistance as well as B-linear magnetoresistance over an extended temperature and magnetic field range in a quantum critical region in the phase diagram. Moreover, the slope of the T-linear resistance α_cp appears bounded by α_cp {\approx} h/2e^2 [1/T]_c^onset where T_c^onset is the temperature at which Cooper pairs form, intimating a common scale-invariant transport mechanism corresponding to Planckian dissipation.In contrast to fermionic systems where the temperature and magnetic field dependent scattering rates combine in quadrature of {\hbar}/τ {\approx} {\sqrt} (((k_B T)^2+(μ_B B)^2)), both terms linearly combine in the present bosonic system, i.e. {\hbar}/τ {\approx} (k_B T+[γμ]_B B), where γ is a constant. By extending the reach of strange metal phenomenology to a bosonic system, our results suggest that there is a fundamental principle governing their transport which transcends particle statistics.
Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite N, beyond the large-N used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the ωlnω type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via 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 d-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above 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 T-linear resistivity above 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 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.
Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. 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.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.