We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at $\frac{1}{3}$ filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens. Matter 8, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LL's a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LL's. Possible connections to the newly discovered liquid crystalline phases in higher LL's are also discussed.We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at $\frac{1}{3}$ filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens. Matter 8, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LL's a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LL's. Possible connections to the newly discovered liquid crystalline phases in higher LL's are also discussed.

arXiv:cond-mat/0108119Physical review. B, Condensed matterDec 28, 200116 citations

Quantum Hall states of high symmetry

Chetan Nayak, Frank A. Wilczek

arXiv:cond-mat/9501052Nuclear Physics BSep 1, 19956 citations

Infinite symmetry in the quantum Hall effect

Andrea Cappelli A, Carlo A. Trugenberger, Guillermo R. Zemba

arXiv:hep-th/9206027Nuclear Physics BMay 1, 1993216 citations

Single-mode approximation for quantum Hall states with broken rotational symmetry

Ruizhi Qiu, Zi-Xiang Hu, Xin Wan

A topological phase can often be represented by a corresponding wave function (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wave function fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We show that the single-mode approximation can introduce a variational parameter for a better description of the ground state, which is consistent with the recently proposed geometric description of the quantum Hall phases.A topological phase can often be represented by a corresponding wave function (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wave function fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We show that the single-mode approximation can introduce a variational parameter for a better description of the ground state, which is consistent with the recently proposed geometric description of the quantum Hall phases.

arXiv:1304.2856Physical Review BDec 17, 20135 citations

Conformal symmetry and universal properties of quantum Hall states

Andrea Cappelli A, Gerald V. Dunne, Carlo A. Trugenberger +1 more

arXiv:hep-th/9211071Nuclear Physics BJun 1, 1993104 citations

Microscopic Model for Fractional Quantum Hall Nematics

Songyang Pu, Ajit Coimbatore Balram, Joseph C. Taylor +2 more

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

arXiv:2401.17352Physical Review LettersJun 5, 202421 citations

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at

\frac{1}{3}

filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens. Matter 8, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LL's a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LL's. Possible connections to the newly discovered liquid crystalline phases in higher LL's are also discussed.