Abstract
This paper proposes a fractonic superfluid, in which both particle number and total dipole moments are conserved. The minimal Hamiltonian hence becomes quartic and the associated Gross-Pitaevskii equations become highly nonlinear, with the classical ground states made of plane waves, and quantum fluctuations leading to lower critical dimensions $d=2$.
Highlights
Liquid helium-4 [1,2] is a typical quantum many-boson system described by a Ginzburg-Landau theory
Superfluidity is established with formation of an off-diagonal long range order (ODLRO) [3] and emergence of gapless Goldstone modes
Achievements have been made on a variety of physical properties of superfluidity; superfluids serve as a platform for different fields, e.g., condensed matter, nuclear physics and high-energy physics [4,5,6,7,8,9,10,11,12,13,14,15,16]
Summary
Liquid helium-4 [1,2] is a typical quantum many-boson system described by a Ginzburg-Landau theory. When chemical potential is turned to positive value, the energy functional drops down to minima when φ belongs to plane-wave configurations, in contrast to conventional superfluid where φ of minima is exactly constant everywhere, i.e., momentum k = 0 This class of configurations with lowest energy constitutes the classical ground-state manifold of fractonic superfluid, and the corresponding timedependent Gross-Pitaevskii equations can be obtained in the presence of such exotic boson condensate. Since quantum fluctuations are not treated seriously, ODLRO of classical ground states is self-consistently established, regardless of dimensions For this purpose, one can integrate out massive amplitude fluctuations, resulting in an effective field theory for phase fluctuations or the gapless Goldstone bosons based on our microscopic many-fracton model. A general many-fracton model is discussed in the Appendix at the end of the paper
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