The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
نویسندگان
چکیده
The structure of ground states of generic FQH states on a torus is studied by using both effective theory and electron wave function. The relation between the effective theory and the wave function becomes transparent when one considers the ground state structure. We find that the non-abelian Berry’s phases of the abelian Hall states generated by twisting the mass matrix are identical to the modular transformation matrix for the characters of Gaussian conformal field theory. We also show that the Haldane-Rezayi spin singlet state has a ten fold ground state degeneracy on a torus which indicates such a state is a non-abelian Hall state.
منابع مشابه
Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros
It has been shown that different Abelian and non-Abelian fractional quantum Hall states can be characterized by patterns of zeros described by sequences of integers Sa . In this paper, we will show how to use the data Sa to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as w...
متن کاملTopological characterization of fractional quantum Hall ground states from microscopic Hamiltonians.
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized q...
متن کاملS-duality constraints on 1D patterns associated with fractional quantum Hall states.
Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g., through the thin torus limit. In the simplest case, these constraints enforce the well-known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degen...
متن کاملSpin in fractional quantum Hall systems
A system at filling factor 2/3 could be a candidate for a quantum Hall ferromagnet at integer filling factor of composite fermions. Using exact diagonalization with electrons on a torus we study the transition from the singlet ground state to the polarized ground state at this filling and look for signatures of quantum Hall ferromagnetism. Differences between the fractional and corresponding in...
متن کاملModular Invariance on the Torus and Fractional Quantum Hall Effect
The implementation of modular invariance on the torus at the quantum level is discussed in a group-theoretical framework. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is ev...
متن کامل