Holographic charge density wave from D2-D8
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Springer
Received: September Revised: February Accepted: April Published: May
10, 13, 16, 22,
2019 2020 2020 2020
Nishal Raia and Subir Mukhopadhyayb a
Department of Physics, SRM University Sikkim, 5th Mile, Tadong, Gangtok, Sikkim, 737102 India b Department of Physics, Sikkim University, 6th Mile, Gangtok, Sikkim, 737102 India
E-mail: [email protected], [email protected] Abstract: We have considered D2-D8 model and obtain a numerical solution that exhibits spatially modulated phases corresponding to a charge density wave and a spin density wave. We have analysed behavior of the free energy density for different values of the chemical potential and the magnetic field. Keywords: Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 1909.03458
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)109
JHEP05(2020)109
Holographic charge density wave from D2-D8
Contents 1 Introduction
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2 D2-D8 model
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3 Spatially modulated solution
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1
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Introduction
There are varieties of condensed matter systems that exhibit spontaneous breaking of spatial symmetry. In particular, some systems admit spatially modulated phases that correspond to the breaking of the translation symmetry and symmetry of the lattice in the ground states. Common examples of such phases are charge and spin density waves [1, 2]. Charge density waves were first predicted [3] for a weakly coupled one-dimensional system. Various metals admit spatially modulated charge density phases. They appear in strongly correlated systems as well and sometimes they are accompanied by spin density waves, as found in the striped phases of high Tc cuprate superconductors [4]. They are characterized by competing orders, which is believed to play an important role in the rich phase structure of high Tc superconductors. Such breaking of translation symmetry modifies the transport behaviors, e.g. showing unconventional behaviors of DC and AC conductivities. Gauge/gravity duality offers a novel method to study the strongly correlated systems by translating problems in a strongly coupled d-dimensional field theory into phenomena of a weakly coupled gravity theory living in (d+1) dimension [5–8]. A number of works have appeared, where this duality has been applied for studying systems with broken symmetry. Solutions with explicitly broken symmetry can be obtained by introducing sources that depend on space, such as chemical potential. On the other hand, sometimes spatially homogeneous solutions in presence of large charge density or magnetic field develop instability leading to spatially modulated configurations. Systems with such instabilities arise in the context of holographic QCD as well as probe brane models. One of the mechanisms of such instability occurs in Maxwell-Chern-Simons theory at non-zero momentum once an electric field is turned on [9]. When coupled to gravity, RN-AdS black hole develops a similar instability in presence of an electric field, which depends on the n
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