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A holographic strange metal with slowly fluctuating translational order
Andrea Amoretti, Daniel Areán, Blaise Goutéraux, Daniele Musso
Abstract: We study the interplay of slowly fluctuating translational order with quantum criticality in a strongly-coupled metallic phase using Gauge/Gravity duality. Upon weak explicit breaking of translations, the Nambu-Goldstone bosons of translational order -- the phonons -- acquire a small complex gap, i.e. both a small mass and relaxation rate. We use a combination of analytical and numerical computations to extract their temperature dependence. At high temperature, the phase is insulating, and accordingly a pinning peak appears in the ac conductivity and moves off-axis as the temperature is lowered. As the system enters the IR critical regime, it becomes metallic with a resistivity linear in temperature. Correspondingly, the off-axis peak reverses direction and eventually becomes Drude-like at the lowest temperatures. Throughout, relaxation of the pseudo-phonons governs the dynamics. A similar transport phenomenology is observed in the phase diagram of bad metals and cuprate strange metals, where translational order and quantum criticality are both believed to play a central role.