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Short distance physics of fractionally quantized Hall fluids

Martin Greiter

Published Jul 1, 1996• 0 citations
OpenAlex

Abstract

In order to obtain a local description of the short-distance physics of fractionally quantized Hall states for realistic (e.g.Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual test electron from far away, as particles.I then present evidence in support of this interpretation, and argue that the electron eectively decomposes into quark-like constituent particles of fractional charge.

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In order to obtain a local description of the short-distance physics of fractionally quantized Hall states for realistic (e.g.Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual test electron from far away, as particles.I then present evidence in support of this interpretation, and argue that the electron eectively decomposes into quark-like constituent particles of fractional charge.
The clustering pattern of zeros in the ground state of a fractional quantum Hall system is a defining feature of its topological properties. We analyze the geometrical fluctuations of the zeros around individual electrons and propose to use the displacement ratio of the zeros to visualize and measure the distance of a realistic state to a model wave function. The distribution of the zero displacement ratio behaves like an order parameter in the transition from a Laughlin phase to a topologically trivial one. The statistical comparison between quantum Hall states belonging to different Jain sequences leads to a composite fermion fluid description of the ν=1/5ν= 1/5ν=1/5 ground state with long-range Coulomb interaction that agrees almost perfectly for as few as 333-555 electrons, overcoming the long-standing difficulties of accommodating the competing liquid and crystal orders at short distances.
Abstract Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. We present a second-quantization framework that reveals an exact fusion mechanism for particle fractionalization in FQH fluids, and uncovers the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level. We show the first exact analytic computation of the quasielectron Berry connections leading to its fractional charge and exchange statistics, and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. We express the sequence of (bosonic and fermionic) Laughlin second-quantized states, highlighting the lack of local condensation, and present a rigorous constructive subspace bosonization dictionary for the bulk fluid. Finally, we establish universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid.
It is shown that the wave function proposed by Tao and Thouless to explain the fractional quantization of the Hall current implies long-range correlations between the electrons that are very different from the properties expected from Laughlin's wave function. Calculations for a small number of electrons have shown that Laughlin's wave function is an excellent approximation to the true ground state, so it must be concluded that the Tao-Thouless wave function is not a good approximation. There is some discussion of the question of broken symmetry.
We provide numerical evidence that the ground state of a short-range-interaction model at \ensuremath{\nu}=1/2 is incompressible and spin singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest-lying spin-singlet state, and propose that fractional quantum Hall effect would occur at \ensuremath{\nu}=1/2 if this state became the global ground state. Some conclusions of an earlier paper are invalidated by the present numerical study of a larger system; these will be indicated.