Auto-tuned large scale quantum hybrid Monte Carlo for clean and dirty itinerant quantum phase transitions and strange metals

We introduce a novel computational method, quantum hybrid Monte Carlo with auto-tuning, for the study of sign-problem-free electronic Hamiltonians. The method particularly shines in the study of itinerant quantum phase transitions, where large system sizes and high accuracy are required to extract universal behavior. We apply the method to the antiferromagnetic (AFM) quantum phase transition in two-dimensional metals, both in the clean case and when the Yukawa interaction is subject to quenched disorder. In the clean case, we uncover strong deviations from Hertz-Millis scaling, consistent with recent analytical predictions. In the disordered case, we find a rich phase diagram, which contains a strange metal phase that shows no residual resistivity and planckian linear-in-temperature scattering that is independent of the disordered interaction strength, as well as a short-range-ordered AFM phase where the residual resistivity increases rapidly and the resistivity receives a logarithmic-in-temperature correction. Our phase diagram bears many similarities to that of cuprates, which suggests that our key ingredients of critical AFM fluctuations plus inhomogeneity in the coupling between the AFM order parameter and the electrons are responsible for much of their mysterious behavior.

Current work on applying the method to the Ising-Nematic phase transition will also be discussed.