Loop current fluctuations and quantum critical transport
Abstract
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.
- Authors:
-
- Massachusetts Institute of Technology
- Harvard University
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1973725
- Grant/Contract Number:
- SC0008739
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics
- Additional Journal Information:
- Journal Name: SciPost Physics Journal Volume: 14 Journal Issue: 5; Journal ID: ISSN 2542-4653
- Publisher:
- Stichting SciPost
- Country of Publication:
- Netherlands
- Language:
- English
Citation Formats
Shi, Zhengyan Darius, Else, Dominic V., Goldman, Hart, and Senthil, Todadri. Loop current fluctuations and quantum critical transport. Netherlands: N. p., 2023.
Web. doi:10.21468/SciPostPhys.14.5.113.
Shi, Zhengyan Darius, Else, Dominic V., Goldman, Hart, & Senthil, Todadri. Loop current fluctuations and quantum critical transport. Netherlands. https://doi.org/10.21468/SciPostPhys.14.5.113
Shi, Zhengyan Darius, Else, Dominic V., Goldman, Hart, and Senthil, Todadri. Mon .
"Loop current fluctuations and quantum critical transport". Netherlands. https://doi.org/10.21468/SciPostPhys.14.5.113.
@article{osti_1973725,
title = {Loop current fluctuations and quantum critical transport},
author = {Shi, Zhengyan Darius and Else, Dominic V. and Goldman, Hart and Senthil, Todadri},
abstractNote = {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 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} σ ( ω > 0 ) ∼ ω − 2 / z , where z 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 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 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} σ ( ω > 0 ) ∼ ω − 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.},
doi = {10.21468/SciPostPhys.14.5.113},
journal = {SciPost Physics},
number = 5,
volume = 14,
place = {Netherlands},
year = {Mon May 15 00:00:00 EDT 2023},
month = {Mon May 15 00:00:00 EDT 2023}
}
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Works referenced in this record:
The Remarkable Underlying Ground States of Cuprate Superconductors
journal, March 2019
- Proust, Cyril; Taillefer, Louis
- Annual Review of Condensed Matter Physics, Vol. 10, Issue 1
Gauge-invariant response functions of fermions coupled to a gauge field
journal, December 1994
- Kim, Yong Baek; Furusaki, Akira; Wen, Xiao-Gang
- Physical Review B, Vol. 50, Issue 24
Theory of the Quantum Critical Fluctuations in Cuprate Superconductors
journal, August 2007
- Aji, Vivek; Varma, C. M.
- Physical Review Letters, Vol. 99, Issue 6
Low-energy properties of fermions with singular interactions
journal, November 1994
- Altshuler, B. L.; Ioffe, L. B.; Millis, A. J.
- Physical Review B, Vol. 50, Issue 19
Continuous Mott transition in semiconductor moiré superlattices
journal, September 2021
- Li, Tingxin; Jiang, Shengwei; Li, Lizhong
- Nature, Vol. 597, Issue 7876
Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions
journal, November 2020
- Mandal, Ipsita
- Physical Review Research, Vol. 2, Issue 4
Gifts from anomalies: Exact results for Landau phase transitions in metals
journal, November 2022
- Shi, Zhengyan; Goldman, Hart; Else, Dominic
- SciPost Physics, Vol. 13, Issue 5
Ergodicity, constants of motion, and bounds for susceptibilities
journal, January 1971
- Suzuki, M.
- Physica, Vol. 51, Issue 2
Finite-temperature properties of quantum Lifshitz transitions between valence-bond solid phases: An example of local quantum criticality
journal, July 2005
- Ghaemi, Pouyan; Vishwanath, Ashvin; Senthil, T.
- Physical Review B, Vol. 72, Issue 2
Low-frequency Raman response near the Ising-nematic quantum critical point: A memory-matrix approach
journal, January 2022
- Wang, Xiaoyu; Berg, Erez
- Physical Review B, Vol. 105, Issue 4
Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
journal, June 2019
- Wang, Xiaoyu; Berg, Erez
- Physical Review B, Vol. 99, Issue 23
Cooper pairing in non-Fermi liquids
journal, March 2015
- Metlitski, Max A.; Mross, David F.; Sachdev, Subir
- Physical Review B, Vol. 91, Issue 11
A Quantum Critical Point Lying Beneath the Superconducting Dome in Iron Pnictides
journal, March 2014
- Shibauchi, T.; Carrington, A.; Matsuda, Y.
- Annual Review of Condensed Matter Physics, Vol. 5, Issue 1
Ultraviolet-Infrared Mixing in Marginal Fermi Liquids
journal, March 2022
- Ye, Weicheng; Lee, Sung-Sik; Zou, Liujun
- Physical Review Letters, Vol. 128, Issue 10
Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+δ
journal, September 2008
- Li, Y.; Balédent, V.; Barišić, N.
- Nature, Vol. 455, Issue 7211
Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
journal, March 2015
- Wu, Tao; Mayaffre, Hadrien; Krämer, Steffen
- Nature Communications, Vol. 6, Issue 1
Quantum critical behaviour in a high-Tc superconductor
journal, September 2003
- Marel, D. van der; Molegraaf, H. J. A.; Zaanen, J.
- Nature, Vol. 425, Issue 6955
Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large- Limit
journal, August 2019
- Damia, Jeremias Aguilera; Kachru, Shamit; Raghu, Srinivas
- Physical Review Letters, Vol. 123, Issue 9
Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions
journal, April 2017
- Schlief, Andres; Lunts, Peter; Lee, Sung-Sik
- Physical Review X, Vol. 7, Issue 2
Anomalous dynamical scaling from nematic and U(1) gauge field fluctuations in two-dimensional metals
journal, July 2015
- Holder, Tobias; Metzner, Walter
- Physical Review B, Vol. 92, Issue 4
Quantum criticality in twisted transition metal dichalcogenides
journal, September 2021
- Ghiotto, Augusto; Shih, En-Min; Pereira, Giancarlo S. S. G.
- Nature, Vol. 597, Issue 7876
Large-
N
journal, September 2022
- Guo, Haoyu; Patel, Aavishkar A.; Esterlis, Ilya
- Physical Review B, Vol. 106, Issue 11
Quantum Boltzmann equation of composite fermions interacting with a gauge field
journal, December 1995
- Kim, Yong Baek; Lee, Patrick A.; Wen, Xiao-Gang
- Physical Review B, Vol. 52, Issue 24
Theory of the half-filled Landau level
journal, March 1993
- Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
- Physical Review B, Vol. 47, Issue 12
Quantum criticality in heavy-fermion metals
journal, March 2008
- Gegenwart, Philipp; Si, Qimiao; Steglich, Frank
- Nature Physics, Vol. 4, Issue 3
Strange Metals as Ersatz Fermi Liquids
journal, August 2021
- Else, Dominic V.; Senthil, T.
- Physical Review Letters, Vol. 127, Issue 8
Detection and Implications of a Time-Reversal Breaking State in Underdoped Cuprates
journal, November 2002
- Simon, M. E.; Varma, C. M.
- Physical Review Letters, Vol. 89, Issue 24
Two-Dimensional Orbital-Like Magnetic Order in the High-Temperature Superconductor
journal, July 2010
- Balédent, V.; Fauqué, B.; Sidis, Y.
- Physical Review Letters, Vol. 105, Issue 2
Low-energy effective theory of Fermi surface coupled with U(1) gauge field in dimensions
journal, October 2009
- Lee, Sung-Sik
- Physical Review B, Vol. 80, Issue 16
Critical drag as a mechanism for resistivity
journal, November 2021
- Else, Dominic V.; Senthil, T.
- Physical Review B, Vol. 104, Issue 20
Absence of Static Loop-Current Magnetism at the Apical Oxygen Site in from NMR
journal, November 2013
- Mounce, A. M.; Oh, Sangwon; Lee, Jeongseop A.
- Physical Review Letters, Vol. 111, Issue 18
Planckian behavior of cuprate superconductors: Reconciling the scaling of optical conductivity with resistivity and specific heat
preprint, January 2022
- Michon, B.; Berthod, C.; Rischau, C. W.
- arXiv
No evidence for orbital loop currents in charge-ordered from polarized neutron diffraction
journal, December 2017
- Croft, T. P.; Blackburn, E.; Kulda, J.
- Physical Review B, Vol. 96, Issue 21
Quantum-Critical Resistivity of Strange Metals in a Magnetic Field
journal, May 2022
- Varma, Chandra M.
- Physical Review Letters, Vol. 128, Issue 20
Quantum chaos on a critical Fermi surface
journal, February 2017
- Patel, Aavishkar A.; Sachdev, Subir
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
Universal T-linear resistivity and Planckian dissipation in overdoped cuprates
journal, November 2018
- Legros, A.; Benhabib, S.; Tabis, W.
- Nature Physics, Vol. 15, Issue 2
Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order
journal, August 2010
- Metlitski, Max A.; Sachdev, Subir
- Physical Review B, Vol. 82, Issue 7
Thermodynamic properties near the onset of loop-current order in high-T c
journal, March 2009
- Grønsleth, M. S.; Nilssen, T. B.; Dahl, E. K.
- Physical Review B, Vol. 79, Issue 9
Transport near the Ising-nematic quantum critical point of metals in two dimensions
journal, April 2014
- Hartnoll, Sean A.; Mahajan, Raghu; Punk, Matthias
- Physical Review B, Vol. 89, Issue 15
Theory of a continuous Mott transition in two dimensions
journal, July 2008
- Senthil, T.
- Physical Review B, Vol. 78, Issue 4
Magnetic Order in the Pseudogap Phase of High- Superconductors
journal, May 2006
- Fauqué, B.; Sidis, Y.; Hinkov, V.
- Physical Review Letters, Vol. 96, Issue 19
Comment on “No evidence for orbital loop currents in charge-ordered from polarized neutron diffraction”
journal, July 2018
- Bourges, P.; Sidis, Y.; Mangin-Thro, L.
- Physical Review B, Vol. 98, Issue 1
Novel magnetic order in the pseudogap state of high- copper oxides superconductors
journal, June 2011
- Bourges, Philippe; Sidis, Yvan
- Comptes Rendus Physique, Vol. 12, Issue 5-6
How non-Fermi liquids cure their infrared divergences
journal, July 2020
- Damia, Jeremias Aguilera; Solís, Mario; Torroba, Gonzalo
- Physical Review B, Vol. 102, Issue 4
Theory of the pseudogap state of the cuprates
journal, April 2006
- Varma, C. M.
- Physical Review B, Vol. 73, Issue 15
Quantum theory of a nematic Fermi fluid
journal, October 2001
- Oganesyan, Vadim; Kivelson, Steven A.; Fradkin, Eduardo
- Physical Review B, Vol. 64, Issue 19
Controlled expansion for certain non-Fermi-liquid metals
journal, July 2010
- Mross, David F.; McGreevy, John; Liu, Hong
- Physical Review B, Vol. 82, Issue 4
Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
journal, March 2023
- Borges, Francisco; Borissov, Anton; Singh, Ashutosh
- Annals of Physics, Vol. 450
Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates
journal, July 2016
- Varma, Chandra M.
- Reports on Progress in Physics, Vol. 79, Issue 8
Observable NMR signal from circulating current order in YBCO
journal, April 2012
- Lederer, Samuel; Kivelson, Steven A.
- Physical Review B, Vol. 85, Issue 15
Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
journal, April 2018
- Klein, Avraham; Lederer, Samuel; Chowdhury, Debanjan
- Physical Review B, Vol. 97, Issue 15
Solvable theory of a strange metal at the breakdown of a heavy Fermi liquid
journal, June 2022
- Aldape, Erik E.; Cookmeyer, Tessa; Patel, Aavishkar A.
- Physical Review B, Vol. 105, Issue 23
Colloquium : Linear in temperature resistivity and associated mysteries including high temperature superconductivity
journal, July 2020
- Varma, Chandra M.
- Reviews of Modern Physics, Vol. 92, Issue 3
Quantum-critical transport of marginal Fermi-liquids
preprint, January 2022
- Maebashi, Hideaki; Varma, Chandra M.
- arXiv
Fermi-liquid instabilities at magnetic quantum phase transitions
journal, August 2007
- Löhneysen, Hilbert v.; Rosch, Achim; Vojta, Matthias
- Reviews of Modern Physics, Vol. 79, Issue 3
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017
- Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2017, Issue 5
Superconducting instability in non-Fermi liquids
journal, September 2016
- Mandal, Ipsita
- Physical Review B, Vol. 94, Issue 11
Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa 2 Cu 3 O y
journal, January 2018
- Zhang, Jian; Ding, Zhaofeng; Tan, Cheng
- Science Advances, Vol. 4, Issue 1
Quantum critical behaviour in magic-angle twisted bilayer graphene
journal, April 2022
- Jaoui, Alexandre; Das, Ipsita; Di Battista, Giorgio
- Nature Physics, Vol. 18, Issue 6
Adventure in Topological Phase Transitions in -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality
journal, May 2019
- Bi, Zhen; Senthil, T.
- Physical Review X, Vol. 9, Issue 2
Gauge theory of the normal state of high- superconductors
journal, September 1992
- Lee, Patrick A.; Nagaosa, Naoto
- Physical Review B, Vol. 46, Issue 9
Non-ergodicity of phase functions in certain systems
journal, September 1969
- Mazur, P.
- Physica, Vol. 43, Issue 4
Topological excitations near the local critical point in the dissipative two-dimensional model
journal, November 2010
- Aji, Vivek; Varma, C. M.
- Physical Review B, Vol. 82, Issue 17
Long-wavelength correlations and transport in a marginal Fermi liquid
journal, January 2009
- Shekhter, A.; Varma, C. M.
- Physical Review B, Vol. 79, Issue 4
Large- theory of critical Fermi surfaces
journal, June 2021
- Esterlis, Ilya; Guo, Haoyu; Patel, Aavishkar A.
- Physical Review B, Vol. 103, Issue 23
Non-Fermi liquid fixed point in 2 + 1 dimensions
journal, April 1994
- Nayak, Chetan; Wilczek, Frank
- Nuclear Physics B, Vol. 417, Issue 3
Cooper pairing of incoherent electrons: An electron-phonon version of the Sachdev-Ye-Kitaev model
journal, September 2019
- Esterlis, Ilya; Schmalian, Jörg
- Physical Review B, Vol. 100, Issue 11
Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
journal, April 2021
- Else, Dominic V.; Thorngren, Ryan; Senthil, T.
- Physical Review X, Vol. 11, Issue 2
Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006
- Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
- Reviews of Modern Physics, Vol. 78, Issue 1
Quantum criticality in dissipative quantum two-dimensional and Ashkin-Teller models: Application to the cuprates
journal, May 2009
- Aji, Vivek; Varma, C. M.
- Physical Review B, Vol. 79, Issue 18
Local quantum criticality in the two-dimensional dissipative quantum XY model
journal, May 2015
- Zhu, Lijun; Chen, Yan; Varma, Chandra M.
- Physical Review B, Vol. 91, Issue 20
Effect of a nonzero temperature on quantum critical points in itinerant fermion systems
journal, September 1993
- Millis, A. J.
- Physical Review B, Vol. 48, Issue 10
Singular charge fluctuations at a magnetic quantum critical point
journal, January 2020
- Prochaska, L.; Li, X.; MacFarland, D. C.
- Science, Vol. 367, Issue 6475
Low-energy dynamics of the spinon-gauge system
journal, July 1994
- Polchinski, Joseph
- Nuclear Physics B, Vol. 422, Issue 3
Universal theory of strange metals from spatially random interactions
preprint, January 2022
- Patel, Aavishkar A.; Guo, Haoyu; Esterlis, Ilya
- arXiv
Phase diagram and correlation functions of the two-dimensional dissipative quantum XY model
journal, November 2016
- Hou, Changtao; Varma, Chandra M.
- Physical Review B, Vol. 94, Issue 20
Dynamic structure function of some singular Fermi liquids
journal, August 2017
- Varma, Chandra M.
- Physical Review B, Vol. 96, Issue 7
Ultraviolet/infrared mixing in non-Fermi liquids
journal, July 2015
- Mandal, Ipsita; Lee, Sung-Sik
- Physical Review B, Vol. 92, Issue 3
Holographic quantum matter
preprint, January 2016
- Hartnoll, Sean A.; Lucas, Andrew; Sachdev, Subir
- arXiv
Strange Metal in Magic-Angle Graphene with near Planckian Dissipation
journal, February 2020
- Cao, Yuan; Chowdhury, Debanjan; Rodan-Legrain, Daniel
- Physical Review Letters, Vol. 124, Issue 7
Perturbative non-Fermi liquids from dimensional regularization
journal, December 2013
- Dalidovich, Denis; Lee, Sung-Sik
- Physical Review B, Vol. 88, Issue 24
Absence of evidence for magnetic order in the pseudogap phase of
journal, May 2020
- Gheidi, S.; Akintola, K.; Fang, A. C. Y.
- Physical Review B, Vol. 101, Issue 18