Bulk/Boundary Relations in Hydrodynamics with Quantum Anomalies

Gustavo M. Monteiro, Alexander G. Abanov

Gustavo M. Monteiro, Dylan Reynolds, Paolo Glorioso +1 more

In this Letter, we investigate the dissipative dynamics at the edge of Laughlin fractional quantum Hall (FQH) states starting from the hydrodynamic framework of the composite boson theory recently developed by G. M. Monteiro et al. [Phys. Rev. B 109, 174525 (2024)]. Critical to this description is the choice of boundary conditions, which ultimately stems from the choice of hydrodynamic variables in condensate degrees of freedom. Given the gapped nature of bulk, one would expect dissipation effects to play an important role only near the FQH edge. Thus, one envisions a scenario where the bulk hydrodynamic equations remain unmodified, while the dissipation effects are introduced at the edge via boundary conditions. We have recently shown that the anomaly requirements fix the boundary conditions of the FQH fluid to be no-penetration and no-stress boundary conditions. In this work, we introduce energy dissipation in the no-stress boundary condition leading to charge diffusion at the boundary. The resulting dissipative edge dynamics is quite rigid from a hydrodynamic perspective, as it has to preserve the edge charge continuity and the anomaly structure. We show that the diffusive edge dynamics with fluctuation-dissipation relations within a power counting scheme belong to the Kardar-Parisi-Zhang universality class.

Bin-Bin Mao, Chenjie Wang

The authors derive an expression for the anomaly indicator which is able to detect quantum anomaly associated with the mirror symmetry in general two dimensional fermionic topological orders. Anomalous topological orders can live only on the surface of 3D topological crystalline superconductors, and the authors' derivation establishes a direct correspondence between properties of the bulk and boundary, namely a bulk-boundary correspondence.

P.G. Mitkin, V. I. ZAKHAROV

Masaru Hongo, Tomoya Hayata, Yoshimasa Hidaka +2 more

Gustavo M. Monteiro, V. P. Nair, Sriram Ganeshan

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 nonlinearly coupled to the edge density, thus systematically extending the edge chiral Luttinger liquid theory.