Magnetotransport and complexity of holographic metal-insulator transitions
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Springer
Received: August Revised: September Accepted: September Published: October
7, 3, 3, 5,
2020 2020 2020 2020
Yu-Sen An,a,b Teng Jia,b and Li Lia,b,c,1 a
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China b School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, China c School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
E-mail: [email protected], [email protected], [email protected] Abstract: We study the magnetotransport in a minimal holographic setup of a metalinsulator transition in two spatial dimensions. Some generic features are obtained without referring to the non-linear details of the holographic theory. The temperature dependence of resistivity is found to be well scaled with a single parameter T0 , which approaches zero at some critical charge density ρc , and increases as a power law T0 ∼ |ρ − ρc |1/2 both in metallic (ρ > ρc ) and insulating (ρ < ρc ) regions in the vicinity of the transition. Similar features also happen by changing the disorder strength as well as magnetic field. By requiring a positive definite longitudinal conductivity in the presence of an applied magnetic field restricts the allowed parameter space of theory parameters. We explicitly check the consistency of parameter range for two representative models, and compute the optical conductivities for both metallic and insulating phases, from which a disorderinduced transfer of spectral weight from low to high energies is manifest. We construct the phase diagram in terms of temperature and disorder strength. The complexity during the transition is studied and is found to be not a good probe to the metal-insulator transition. Keywords: Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 2007.13918 1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)023
JHEP10(2020)023
Magnetotransport and complexity of holographic metal-insulator transitions
Contents 1 Introduction
1
2 Holographic setup
3 5 5 7 9 10 14 16
4 AC conductivity and phase diagram 4.1 Optical conductivity 4.2 Phase diagram, specific heat and charge susceptibility
18 18 19
5 Complexity
24
6 Conclusion and discussion
28
A DC conductivity
30
1
Introduction
The mechanism of metal-insulator transition is one of the oldest, yet one of the fundamentally least understood problems in condensed matter physics. For a period of time in the past it was prevailingly believed that there is even no metal-insulator phase transition in two spatial dimensional systems in zero magnetic field, since all charge carriers are thought to be localized in an infinity large two-dimensional system [1]. While it is an important problem, to understand the metal-insulator transition is difficult both from the practical and the conceptual points of view. It is obvious that
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