Abstract
In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary part of the stress tensor imply that the dual boundary system is a viscoelastic solid. By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse channel. Finally, we discuss how the phonon dynamics affects the charge transport.
Highlights
Are conserved or not [6,7,8,9]
In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term
By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse channel
Summary
We consider the following action which can break translational symmetry of dual field theories [35]. According to the holographic dictionary and standard quantization, the leading order φI(0)(t, xi) = αxI = 0 plays the role of external source that breaks translations explicitly, relaxing the momentum on the field theory side. If we instead set λ = 0 and K = 0, the asymptotic expansion of scalar field will be changed by φI(−1)(t, xi) u In this case, the background solution of φI means that the leading φI(−1)(t, xi)-term associated to the source should be turned off while existing a non-zero expectation value < OI > ∼ φI(0)(t, xi) = αxI. The background solution of φI means that the leading φI(−1)(t, xi)-term associated to the source should be turned off while existing a non-zero expectation value < OI > ∼ φI(0)(t, xi) = αxI This implies the pattern of spontaneous breaking of translational symmetry. The dynamics of Goldstone modes has already been studied in holography [30,31,32,33, 43, 49,50,51] and field theory [52,53,54,55,56,57]
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