Current browse context:
cond-mat.mes-hall
Change to browse by:
References & Citations
Condensed Matter > Mesoscale and Nanoscale Physics
Title: Topological fluids with boundaries and fractional quantum Hall edge dynamics: A fluid dynamics derivation of the chiral boson action
(Submitted on 12 Mar 2022 (v1), last revised 29 Mar 2024 (this version, v3))
Abstract: This paper investigates the bulk and boundary dynamics of Laughlin states, which are modeled using composite boson theory within a fluid dynamics framework. In this work, we adopt an alternative starting point based on a hydrodynamic action with topological terms, which fleshes out the fluid aspects of the Laughlin state manifestly. For a particular choice of the velocity field, the fluid equation for this action is akin to first-order hydrodynamic equations, supplemented with an additional constitutive equation known as the Hall constraint. When a hard wall boundary is present, one of the topological terms in the fluid action triggers anomaly inflow, indicating the presence of gauge anomaly at the edge. The first-order hydrodynamic equations require a second boundary condition which, in the absence of dissipation, can be either a no-slip or a no-stress condition. We find that the no-slip condition, where the fluid adheres to the wall is incompatible with the chiral edge dynamics. On the other hand, the no-stress condition, which allows the fluid to move along the wall without friction, is consistent with the expected chiral edge dynamics of the Laughlin state. Furthermore, our work derives this modified no-stress boundary condition within a variational principle. This is accomplished by incorporating a chiral boson action within the boundary action that is non-linearly coupled to the edge density, thus systematically extending the edge chiral Luttinger liquid theory.
Submission history
From: Gustavo Monteiro [view email][v1] Sat, 12 Mar 2022 21:15:53 GMT (118kb,D)
[v2] Sat, 25 Mar 2023 20:02:21 GMT (22kb)
[v3] Fri, 29 Mar 2024 17:31:08 GMT (24kb)
Link back to: arXiv, form interface, contact.