Superfluid hydrodynamics of inhomogeneous states: Systems with broken gauge-translation-symmetry

Alexander V. Prozorkevich, V. L. Samorodov, S. A. Smolyanskiǐ

S. A. Smolyanskiǐ

Johannes Hofmann, W. Zwerger

Abstract We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.

Masakazu Ichiyanagi

A Boss system has two broken symmetries, namely the gauge symmetry and the Galilei translation symmetry. We discuss the microscopic background of the ansatz that the superfluid flow is the manifestation of the local gauge invariance. To do this we show that the depletion velocity fields are the Goldstone fields due to the breakdown of the Galilei translation symmetry. A connection between a Bose-Einstein condensation and superfluid flow is also discussed.

Vincenzo Alba, Bruno Bertini, Maurizio Fagotti +2 more

Abstract We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.