The magnetic effect on a strongly correlated system with two currents near the quantum critical point from holography

Jaeha Lee,Sang-Jin Sin,Geunho Song

doi:10.1093/ptep/ptab028

Abstract

Abstract We study the magnetic effect in a strongly interacting system with two conserved currents near the quantum critical point (QCP). For this purpose, we introduce the hyper-scaling violation geometry with the black hole. Considering the perturbation near the background geometry, we compute the transport coefficients using holographic methods. We calculated the magneto-transport for general QCP and discuss the special point $(z,\theta)=(3/2,1)$, where the data of Dirac material have previously been well described.

Highlights

For a strongly correlated system, the particle nature is often absent so that theories based on quasiparticles such as Landau–Fermi liquid theory fail
Any Dirac fluid can be strongly correlated as far as it has a small Fermi surface, which has already been shown in clean graphene [1,2] and in the surface of a topological insulator with magnetic doping [3,4,5]
We consider the quantum critical point (QCP), where the microscopic details in ultraviolet (UV) are irrelevant and most of the information in UV is apprently lost in a low-energy probe in the sense of coarse graining

Summary

Introduction

For a strongly correlated system, the particle nature is often absent so that theories based on quasiparticles such as Landau–Fermi liquid theory fail. We need a two-current model [6,7]: when the electron and hole densities fluctuate from their equilibrium states, the system is supposed to reduce the difference by creating or absorbing an electron pair: e− ↔ e− + h+ + e−, h+ ↔ h+ + h+ + e−. In this process, energy and momentum should be conserved. We start from a four-dimensional action with asymptotically hyperscaling geometry gμν, which includes a dilaton field φ, a gauge field Aμ to complete the asymptotic hyperscaling violating geometry, two extra gauge fields Bμ(a) which are dual to two conserved currents, and the axion fields χ1, χ2 to break the translational symmetry:

Viγ eγ φ

We can define the radially conserved currents by

Findings

Conclusion