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Physical review. B./Physical review. B

Breakdown of hydrodynamics in a Galilean quantum Hall crystal

Xiaoyang Huang, Andrew Lucas

Published Apr 8, 2025• 2 citations
Publisher

Abstract

Strongly interacting quantum Hall liquids can spontaneously break translational symmetry, forming a quantum Hall (Wigner) crystal. Here, the authors investigate its finite-temperature out-of-equilibrium dynamics, and show that nonlinear fluctuations drive the system to an unusual dynamical universality class, analogous to a ``fracton fluid''. The authors provide supporting numerical evidence and propose experimental observation of this phenomenon in high-quality GaAs heterostructures using microwave impedance microscopy.

DOI
10.1103/physrevb.111.l161107

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Strongly interacting quantum Hall liquids can spontaneously break translational symmetry, forming a quantum Hall (Wigner) crystal. Here, the authors investigate its finite-temperature out-of-equilibrium dynamics, and show that nonlinear fluctuations drive the system to an unusual dynamical universality class, analogous to a ``fracton fluid''. The authors provide supporting numerical evidence and propose experimental observation of this phenomenon in high-quality GaAs heterostructures using microwave impedance microscopy.
We construct a nonlinear fluctuating hydrodynamic effective field theory for Galilean-invariant quantum Hall systems with spontaneously broken translational symmetry. Neglecting the role of energy conservation in a low-temperature regime, the hydrodynamic mode is a magnetophonon with quartic attenuation: ω∼±k2−ikzω\sim \pm k^2-\mathrm{i} k^zω∼±k2−ikz with z=4z=4z=4. However, this linear response theory is unstable, and flows to a non-trivial dynamical universality class with z≈3z\approx 3z≈3. We observe this scaling in numerical simulations of many-body classical Hamiltonian dynamics, in a model of an electronic crystal in the lowest Landau level. Observing this magnetophonon decay rate in a quantum Hall crystal represents a promising setting to detect an analogue of a "fractonic dynamical universality class" in a solid-state system, e.g. using microwave impedance microscopy.
Abstract The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.
Collective excitations are crucial for understanding exotic phases and phase transitions in quantum many-body systems. In this work, we numerically demonstrate the microscopic realization of a transition from a translationally invariant fractional quantum anomalous Hall (FQAH) state to a spontaneously broken-translation-symmetry FQAH state, driven by softening of the magnetoroton mode via isotropic interactions in a topological flat-band model. At the critical point, the neutral excitation gap closes at finite momentum, while the charge gap remains stable. This transition shares similarities with Landau-level quantum Hall crystals and nematics but exhibits unique features. Criticality analysis shows that this non-trivial transition belongs to the Ising universality class. Such spontaneous translation symmetry breaking within a topologically ordered FQAH state could serve as a universal mechanism across various systems, with potential implications for quantum moiré materials and cold-atom systems.
We show that dirty quantum Hall systems exhibit large hydrodynamic fluctuations at their edge that lead to anomalously damped charge excitations in the Kardar-Parisi-Zhang universality class ω≃ck-iDk^{3/2}. The dissipative optical conductivity of the edge is singular at low frequencies σ(ω)∼1/ω^{1/3}. These results are direct consequences of the charge continuity relation, the chiral anomaly, and thermalization on the edge-in particular translation invariance is not assumed. Diffusion of heat similarly breaks down, with a universality class that depends on whether the bulk thermal Hall conductivity vanishes. We further establish the theory of fluctuating hydrodynamics for surface chiral metals, where charge fluctuations give logarithmic corrections to transport.
We study the temporal behavior of topological quantum fluids with strong long-range couplings under slow external perturbations, whose rate δδδ approaches the quasi-static limit δ→0δ\to 0δ→0. As expected, due to strong long-range interactions, the system lies in the mean-field universality and the density of defects for drives across the quantum critical point is adiabatic nexc∝δ2n_{\rm exc}\propto δ^{2}nexc​∝δ2. However, if the drive is instead terminated precisely at the edge of the topological non-trivial phase, the number of generated excitations becomes extensive nexc∝O(1)n_{\rm exc}\propto O(1)nexc​∝O(1). This result fundamentally breaks the established universal behavior observed in local topological quantum fluids and demonstrates a novel mechanism for the breakdown of adiabaticity in fermionic systems with strong long-range interactions.
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms.