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arXiv:2305.06421 · Physical review. B./Physical review. B

Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte Carlo study

Rafael M. P. Teixeira, C. Pépin, Hermann Freire

Published Aug 22, 2023• 3 citations
arXivHTMLPDF

Abstract

We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via ${Z}_{2}$ 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 ${T}_{c}$, 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 ${T}_{c}$ 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 ${Z}_{2}$ 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.

DOI
10.1103/physrevb.108.085131

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In the last few decades, quantum criticality in itinerant electron systems has become a central focus of condensed matter physics. On the one hand, it represents a candidate mechanism for high-temperature superconductivity. On the other hand, it can lead to a breakdown of Fermi liquid theory. The formation of a comprehensive understanding of metallic quantum criticality has, however, been significantly hampered by the fact that in many-fermion systems, fluctuations of a critical order parameter can couple to extensive gapless modes on a finite Fermi surface. This interplay, while giving rise to intriguing physical phenomena, leads to strong electronic correlations, which are notoriously difficult to handle by analytic methods. In this thesis, we investigate metallic quantum criticality by means of large-scale quantum Monte Carlo simulations and contribute unbiased, rigorous results to the discussion. Focusing on antiferromagnetic spin-density wave ordering, we present the numerically exact phase diagram of a spin-fermion model whose solution has so far been out of reach. In particular, we highlight the emergence of high-temperature d-wave superconductivity and rigorously establish the quantum critical properties of the antiferromagnetic quantum critical point. Combining the Monte Carlo method with a quantum loop topography approach, we demonstrate that important features of quantum critical metals can be autonomously identified by machine learning of current-current correlations. This allows us to analyze the electronic transport characteristics of two quantum critical metals, including the spin-fermion model, over a large parameter range and leads to the identification of extended non-Fermi liquid regimes in their respective phase diagrams.
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Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
One of the most challenging problems in computational condensed matter physics is the simulation of many-electron systems by unbiased numerical techniques. Quantum Monte Carlo approaches – typically the method of choice for quantum many-body systems with bosonic or spin degrees of freedom – are oftentimes limited to handle many-electron systems due to the infamous fermion-sign problem that severely limits the computational efficiency of this otherwise very potent class of algorithms. Here we report on an elegant approach to overcome the fermion-sign problem in the study of competing quantum magnetism and superconductivity in metals. This approach allows us to study the onset of spin-density wave order in such itinerant electron systems via two-dimensional lattice models amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of these models reveal a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. The striking similarity of these numerical results to the experimentally observed phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.
“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.
We report on numerically exact determinantal quantum Monte Carlo simulations of the onset of spin-density-wave (SDW) order in itinerant electron systems captured by a sign-problem-free two-dimensional lattice model. Extensive measurements of the SDW correlations in the vicinity of the phase transition reveal that the critical dynamics of the bosonic order parameter are well described by a dynamical critical exponent z=2z=2z=2, consistent with Hertz-Millis theory, but are found to follow a finite-temperature dependence that does not fit the predicted behavior of the same theory. The presence of critical SDW fluctuations is found to have a strong impact on the fermionic quasiparticles, giving rise to a dome-shaped superconducting phase near the quantum critical point. In the superconducting state we find a gap function that has an opposite sign between the two bands of the model and is nearly constant along the Fermi surface of each band. Above the superconducting Tc{T}_{c}Tc​, our numerical simulations reveal a nearly temperature and frequency independent self-energy causing a strong suppression of the low-energy quasiparticle weight in the vicinity of the hot spots on the Fermi surface. This indicates a clear breakdown of Fermi liquid theory around these points.