[论文解读] Ideal fracton superfluids

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

Quantum many-body systems参考文献 79被引用 12

一句话总结

本文通过对 fracton 代数进行 gauging 以获得 Aristotelian geometry，建立了 fracton 系统的流体力学框架；证明具有非零电荷密度的平衡态需要自发破缺 fractonic 对称性，并识别出两类主要的 fracton superfluid（p-wave 和 s-wave），它们具有不同的理想阶谱和谱域。

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.

研究动机与目标

• 在曲率空间中提出并构建具有守恒偶极矩的 fracton 相的一致热力学与流体力学描述。
• 通过对 fracton 代数进行 gauging 将 fracton 场论与 Aristotelian geometry 相耦合并推导 Ward 恒等式。
• 确定是否存在具有非零电荷密度和流动的全局热态，并对由对称性破缺引发的 fracton 超流相进行分类。

提出的方法

• 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.

实验结果

研究问题

• 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?

主要发现

• 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.