Abstract
We present a dissipative hydrodynamic theory of “s-wave dipole superfluids” that arise in phases of translation-invariant and dipole-symmetric models in which the U(1) symmetry is spontaneously broken. The hydrodynamic description is subtle on account of an analogue of dangerously irrelevant operators, which requires us to formalize an entirely new derivative counting scheme suitable for these fluids. We use our hydrodynamic model to investigate the linearized response of such a fluid, characterized by sound modes ω ~ ±k – ik2, shear modes ω ~ –ik2, and magnon-like propagating modes ω ~ ±k2 – ik4 that are the dipole-invariant version of superfluid “second sound” modes. We find that these fluids can also admit equilibrium states with “dipole superflow” that resemble a polarized medium. Finally, we couple our theory to slowly varying background fields, which allows us to compute response functions of hydrodynamic operators and Kubo formulas for hydrodynamic transport coefficients.
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Acknowledgments
We are grateful to Jay Armas, Blaise Gouteraux, Andrew Lucas, Matthew Roberts, and Charles Stahl for helpful discussions. The work of KJ, RL, and EM was supported in part by the NSERC Discovery Grant program of Canada. The work of AJ was funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement NonEqbSK No. 101027527. AJ is also partly supported by the Netherlands Organization for Scientific Research (NWO) and by the Dutch Institute for Emergent Phenomena (DIEP) cluster at the University of Amsterdam. Part of this project was carried out during “The Many Faces of Relativistic Fluid Dynamics” and the “Quantum Materials With and Without Quasiparticles” programs at KITP, Santa Barbara, supported by the National Science Foundation under Grant No. NSF PHY-1748958 and PHY-2309135.
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Jain, A., Jensen, K., Liu, R. et al. Dipole superfluid hydrodynamics. Part II.. J. High Energ. Phys. 2024, 197 (2024). https://doi.org/10.1007/JHEP07(2024)197
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DOI: https://doi.org/10.1007/JHEP07(2024)197