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Gifts from anomalies: Exact results for Landau phase transitions in metals
by Zhengyan Darius Shi, Hart Goldman, Dominic V. Else, T. Senthil
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Hart Goldman · Zhengyan Shi |
| Submission information | |
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| Preprint Link: | scipost_202208_00073v1 (pdf) |
| Date accepted: | 2022-09-06 |
| Date submitted: | 2022-08-26 05:31 |
| Submitted by: | Shi, Zhengyan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in "Hertz-Millis" theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, $\mathbf{q}=0$, is a constant independent of frequency, and the real part of the optical conductivity, $\sigma(\omega)$, is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.
Author comments upon resubmission
We posted our detailed responses and manuscript revisions under the "Reply to the above Report" section below each report. Note that all equation references are to the originally submitted manuscript.
List of changes
1. In the Discussion section, we added some comments comparing our results to the DQMC studies of metallic quantum critical points mentioned by Referee 2 (Ilya Esterlis).
2. In Section 4.1, we added a reference to relevant chapters of the classic lecture notes [Goldenfeld, CRC Press, 2018] that contextualize our discussion of conductivity scaling.
3. In Section 6, below eq. (6.8), we have replaced the notation r with the notation m_c^2 used elsewhere in the text.
Published as SciPost Phys. 13, 102 (2022)