Adiabatic Construction of Hierarchical Quantum Hall States

Abstract

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions ν = p/(p(m − 1) + 1) with m odd, from integer Hall states at ν = p through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.

Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions

“…The existence of this "special" parent Hamiltonian allows one to understand a large amount of the physics of the corresponding phase of matter [40]. While such Hamiltonians have been shown to exist for the unprojected CF wave functions [79,80], it is still not known any exist for the projected CF wave functions [81]. Thus, it is still not known, in general, if much of the same physics still applies to the CF wave functions, which is well understood for trial wave functions that do have "special" parent Hamiltonians, as mentioned in the introduction.…”

Bulk-edge Correspondence in the Adiabatic Heuristic Principle

“…Meanwhile, augmented by the symmetry, this notion leads to more unified picture exemplified by the "periodic table" for topologically nontrivial states [7][8][9][10] and demonstrates the existence of rich topological phases. The adiabatic deformation also gives a useful way to characterize concrete models by reducing them to simple systems [11][12][13][14][15][16][17].…”

“…The adiabatic heuristic argument of the quantum Hall (QH) effect [11][12][13] is the historical example in which the adiabatic deformation has been successfully used. The fractional QH (FQH) effect [18,19] is a topological ordered phase [20] with fractionalized excitations [21][22][23].…”

“…Even though it is intrinsically a many-body problem of correlated electrons unlike the integer QH (IQH) effect [1,[24][25][26], the composite fermion theory [27,28] gives a unified scheme to describe their underlying physics: the FQH state at the filling factor ν = p/(2mp ± 1) with p, m integers can be interpreted as the ν = p IQH state of the composite fermions. By continuously trading the external flux for the statistical one [29,30], both states are adiabatically connected through intermediate systems of anyons (adiabatic heuristic principle [11][12][13]). Even though the ground state degeneracy [31,32] is wildly changed in the periodic geometry [12,33], the energy gap remains open and its many-body Chern number [34] works well as an adiabatic invariant [33].…”