Loop current fluctuations and quantum critical transport
We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the ``Hertz-Millis'' type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conduct...
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| Format: | Article |
| Language: | English |
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SciPost
2023-05-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.5.113 |
| _version_ | 1797826570662969344 |
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| author | Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil |
| author_facet | Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil |
| author_sort | Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil |
| collection | DOAJ |
| description | We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the ``Hertz-Millis'' type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $\sigma(\omega>0)\sim\omega^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting ``anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical $N = 1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $\sigma(\omega>0) \sim \omega^{-2(z-2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter. |
| first_indexed | 2024-04-09T12:34:31Z |
| format | Article |
| id | doaj.art-9e01ed394c4d44058601c492d3051833 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T12:34:31Z |
| publishDate | 2023-05-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-9e01ed394c4d44058601c492d30518332023-05-15T16:21:23ZengSciPostSciPost Physics2542-46532023-05-0114511310.21468/SciPostPhys.14.5.113Loop current fluctuations and quantum critical transportZhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. SenthilWe study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the ``Hertz-Millis'' type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $\sigma(\omega>0)\sim\omega^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting ``anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical $N = 1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $\sigma(\omega>0) \sim \omega^{-2(z-2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.https://scipost.org/SciPostPhys.14.5.113 |
| spellingShingle | Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil Loop current fluctuations and quantum critical transport SciPost Physics |
| title | Loop current fluctuations and quantum critical transport |
| title_full | Loop current fluctuations and quantum critical transport |
| title_fullStr | Loop current fluctuations and quantum critical transport |
| title_full_unstemmed | Loop current fluctuations and quantum critical transport |
| title_short | Loop current fluctuations and quantum critical transport |
| title_sort | loop current fluctuations and quantum critical transport |
| url | https://scipost.org/SciPostPhys.14.5.113 |
| work_keys_str_mv | AT zhengyandariusshidominicvelsehartgoldmantsenthil loopcurrentfluctuationsandquantumcriticaltransport |