Abstract
We study the linear stability of holographic homogeneous solids (HHS) at finite temperature and in presence of a background shear strain by means of a large scale quasi-normal mode analysis which extends beyond the hydrodynamic limit. We find that mechanical instability can arise either as a result of a complex speed of sound — gradient instability — or of a negative diffusion constant. Surprisingly, the simplest HHS models are linearly stable for arbitrarily large values of the background strain. For more complex HHS, the onset of the diffusive instability always precedes that of the gradient instability, which becomes the dominant destabilizing process only above a critical value of the background shear strain. Finally, we observe that the critical strains for the two instabilities approach each other at low temperatures. We conclude by presenting a phase diagram for HHS as a function of temperature and background shear strain which shows interesting similarities with the physics of superfluids in presence of background superfluid velocity.
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Acknowledgments
We would like to thank Yuliang Jin, Deng Pan and Yun-Jiang Wang for helpful discussions. This work is supported by the National Natural Science Foundation of China (NSFC) under Grant No.12075298, No.12122513, No.12275038 and No.12047503. M.B. acknowledges the support of the Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01) and the sponsorship from the Yangyang Development Fund. W.J.L is grateful for the financial support from the Fundamental Research Funds for the Central Universities (Grant No.DUT22LK07). W.J.L would also like to thank Institute of Theoretical Physics, Chinese Academy of Sciences for the nice hospitality and the sponsorship from the Peng Huanwu Visiting Professor Program in 2023.
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Baggioli, M., Li, L., Li, WJ. et al. Mechanical stability of homogeneous holographic solids under finite shear strain. J. High Energ. Phys. 2024, 198 (2024). https://doi.org/10.1007/JHEP05(2024)198
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DOI: https://doi.org/10.1007/JHEP05(2024)198