[Paper Review] Ideal fracton superfluids

Jay Armas, Emil Have|arXiv (Cornell University)|Apr 19, 2023

Quantum many-body systems79 references12 citations

TL;DR

The paper develops a hydrodynamic framework for fracton systems by gauging the fracton algebra to obtain Aristotelian geometry, proving that equilibrium states with nonzero charge density require spontaneous breaking of fractonic symmetries, and identifying two main fracton superfluid classes (p-wave and s-wave) with distinct ideal-order spectra and regimes.

ABSTRACT

We investigate the thermodynamics of equilibrium thermal states and their near-equilibrium dynamics in systems with fractonic symmetries in arbitrary curved space. By explicitly gauging the fracton algebra we obtain the geometry and gauge fields that field theories with conserved dipole moment couple to. We use the resultant fracton geometry to show that it is not possible to construct an equilibrium partition function for global thermal states unless part of the fractonic symmetries is spontaneously broken. This leads us to introduce two classes of fracton superfluids with conserved energy and momentum, namely $p$-wave and $s$-wave fracton superfluids. The latter phase is an Aristotelian superfluid at ideal order but with a velocity constraint and can be split into two separate regimes: the U(1) fracton superfluid and the pinned $s$-wave superfluid regimes. For each of these classes and regimes we formulate a hydrodynamic expansion and study the resultant modes. We find distinctive features of each of these phases and regimes at ideal order in gradients, without introducing dissipative effects. In particular we note the appearance of a sound mode for $s$-wave fracton superfluids. We show that previous work on fracton hydrodynamics falls into these classes. Finally, we study ultra-dense $p$-wave fracton superfluids with a large kinetic mass in addition to studying the thermodynamics of ideal Aristotelian superfluids.

Motivation & Objective

• Motivate and construct a consistent thermodynamic and hydrodynamic description of fracton phases with conserved dipole moments in curved space.
• Couple fracton field theories to Aristotelian geometry through gauging the fracton algebra and derive Ward identities.
• Identify whether global thermal states with nonzero charge density and flow exist, and classify fracton superfluid phases arising from symmetry breaking.

Proposed method

• Explicitly gauge the fracton algebra to derive the Aristotelian background geometry and the fracton gauge fields B_mu and A_mu_nu.
• Derive the Ward identities and conservation laws from symmetry principles in curved space.
• Construct equilibrium partition functions for fracton hydrodynamics with conserved dipole moment.
• Introduce and analyze two classes of fracton superfluids (p-wave and s-wave) with associated Goldstone modes and gradient counting.
• Study ideal-order linear perturbations to obtain mode spectra for each phase and regime.

Experimental results

Research questions

• RQ1 Can equilibrium thermal states exist with nonzero charge density and fluid flow in fracton systems, given symmetry constraints?
• RQ2 What are the spontaneous symmetry breaking patterns for fracton symmetries, and how do they define distinct fracton superfluid classes?
• RQ3 What are the ideal-order hydrodynamic modes for p-wave and s-wave fracton superfluids in curved and flat backgrounds?
• RQ4 How does the coupling to Aristotelian geometry constrain gradients and transport in fracton hydrodynamics?
• RQ5 How do previous fracton hydrodynamics frameworks fit into the p-wave and s-wave classifications identified here?

Key findings

• Fracton fluids cannot flow with nonzero charge density unless the fractonic symmetry is spontaneously broken.
• Two classes of fracton superfluids emerge: p-wave (dipole symmetry broken, vector Goldstone) and s-wave (U(1) and dipole broken, scalar and vector Goldstones).
• In p-wave fracton superfluids, ideal-order dynamics lack a sound mode and show magnon-like dispersion with velocity and attenuation parameters.
• In s-wave fracton superfluids, two regimes (U(1) fracton superfluid and pinned s-wave fracton superfluid) feature sound modes and magnon modes with distinct velocities and attenuations.
• The framework unifies and situates prior fracton hydrodynamics results within the p-wave and s-wave classifications.
• Ultra-dense p-wave fracton superfluids with large kinetic mass are studied alongside ideal Aristotelian superfluids.