Abstract
We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At , bosonic and fermionic self-energies are traditionally computed within Eliashberg theory, and they obey scaling relations with characteristic power laws. Corrections to Eliashberg theory break these power laws but only at very small frequencies. Quantum Monte Carlo (QMC) simulations have shown that, already at much larger frequencies, there are strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite and argue that in the range accessible in the QMC simulations above the superconducting transition, the scaling forms for both fermionic and bosonic self-energies are quite different from those at . We compare finite results with QMC data and find good agreement for both systems. We argue that this agreement resolves the key apparent contradiction between the theory and the QMC simulations.
- Received 24 March 2020
- Revised 4 June 2020
- Accepted 8 July 2020
DOI:https://doi.org/10.1103/PhysRevX.10.031053
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
For many years, electrons in metals were assumed to behave, at least qualitatively, as nearly free, weakly interacting particles. Such behavior is termed a Fermi liquid. In recent years, it has become clear that this does not hold in metals near a transition into a state that spontaneously breaks certain symmetries. Near such a transition, electron behavior becomes highly incoherent, almost diffusive. Here, we resolve apparent contradictions between the theory used to describe such non-Fermi-liquid behavior and computer simulations of electron behavior near these transitions.
Traditionally, non-Fermi-liquid behavior is described within strong-coupling Eliashberg theory, a theory that describes how quantized excitations in a solid can bring pairs of electrons together to induce superconductivity. The theory has its limitations but was assumed to work well over a wide range of electron energies. It came as a surprise when unbiased quantum Monte Carlo simulations showed that well within this range of energies there are strong deviations from theoretical predictions, casting doubt on the seemingly solid theoretical analysis.
We resolve the apparent contradiction by accounting for finite-temperature properties of interacting electrons that are not included in the traditional Eliashberg theory. We find that a properly modified theory is in good agreement with quantum Monte Carlo data. We verify this for fermions on the verge of two kinds of ordered states: itinerant antiferromagnetism and electronic nematicity (which breaks lattice rotational symmetry).
Our work will allow analytical theory and numerical tools to be used in synergy to identify and characterize properties of strongly correlated metals.
