Hall Viscosity of Hierarchical Quantum Hall States

Abstract

Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter $\tau$, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor $\nu =2/5$ Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex $\tau$-plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.

References in corpus (8)

• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Quantum Hall system in Tao-Thouless limit
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Microscopic theory of the quantum Hall hierarchy
• Conformal Field Theory of Composite Fermions
• Quantum Hall wave functions on the torus
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions

Cited by in corpus (32)

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• Geometry of Fractional Quantum Hall Fluids
• Viscoelastic response of topological tight-binding models in two and three dimensions
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Geometric adiabatic transport in quantum Hall states
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Composite Fermions on a Torus
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Microscopic Model for Fractional Quantum Hall Nematics
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Berry curvature and Hall viscosities in an anisotropic Dirac semi-metal
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Energy projection and modified Laughlin states
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Laughlin states and their quasi-particle excitations on the torus
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Hall Viscosity of Composite Fermions
• Hall Viscosity and Momentum Transport in Lattice and Continuum Models of the Integer Quantum Hall Effect in Strong Magnetic Fields
• Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
• Success and failure of the plasma analogy for Laughlin states on a torus
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Composite anyons on a torus
• Boson-fermion duality in a gravitational background
• Geometry and large N limits in Laughlin states
• On the modular covariance properties of composite fermions on the torus
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
• Geometric and computational aspects of chiral topological quantum matter
• Coherent State Wave Functions on the Torus