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arXiv:1812.05631 · Physical review. B./Physical review. B

Probing transport in quantum many-fermion simulations via quantum loop topography

Yi Zhang, Carsten Bauer, Peter Broecker, Simon Trebst, Eun-Ah Kim

Published Apr 30, 2019• 5 citations
arXivHTMLPDF

Abstract

Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. Here, the authors demonstrate that quantum loop topography can be used to probe efficiently and directly challenging transport properties by machine learning imaginary-time current-current correlations in quantum Monte Carlo simulations. Applications on the emergence of superconducting fluctuations in the negative-$U$ Hubbard model and a spin-fermion model for a metallic quantum critical point detect changes in transport in good agreement with their established phase diagrams.

DOI
10.1103/physrevb.99.161120

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Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. Here, the authors demonstrate that quantum loop topography can be used to probe efficiently and directly challenging transport properties by machine learning imaginary-time current-current correlations in quantum Monte Carlo simulations. Applications on the emergence of superconducting fluctuations in the negative-UUU Hubbard model and a spin-fermion model for a metallic quantum critical point detect changes in transport in good agreement with their established phase diagrams.
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.