Abstract
Using an algebra of second-quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor n/(2np+1), with integer n and (half-)integer p. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish the organizing "entangled Pauli principle" behind the resulting zero mode paradigm and unveil an emergent SU(n) symmetry characteristic of the fixed point physics of the Jain quantum Hall fluid.
Highlights
Published by the American Physical SocietyIt will turn out that the algebra Z generates all possible ZMs when acting on the incompressible ground state
Introduction.—The fractional quantum Hall (FQH) effect enjoys a unique position in strongly correlated electron physics both as a fascinating physical effect [1] as well as a central juncture for the percolation of ideas between correlated electron physics and other areas of theoretical and mathematical physics
This is the case when the construction of a parent Hamiltonian [4,5,10,11] is possible that falls into what we term the “zero mode (ZM) paradigm”: The zero mode space of a positive semidefinite Hamiltonian is composed of an incompressible state as well as edge or quasihole excitations, where the counting of ZMs in each angular momentum sector precisely matches [6,12,13] the mode counting in the conformal edge theory
Summary
It will turn out that the algebra Z generates all possible ZMs when acting on the incompressible ground state In that sense they are related to the first-quantized pfoorsmsiablliesmthedriescbuescsaeudsebyPSnat−1⁄4o10nepak[;5a5[]wfhoirchth,efoLranug1⁄4hl1inLsLta,teis, really all Eq (4) boils down to] has a simple first-quantized interpretation: It multiplies many-body power-sum symmetric polynomials pz waPve 1⁄4. N 1⁄4 2 state in the class of states jΨn;p;Ni has the wave function ðz1 − z2Þ2pðz1 − z2Þ, or, in second quantization, jΨn;p;2i This state has angular momentum 2J 1⁄4 2p − 1, and the only Tr operators that could possibly not annihilate it are of the form r 0;1;J
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