FQHE: using non-Hermitian operators as constrains for ED
Dear ALPS developers, Some background on the problem I have: --------------------------------------------------- I wish to use the exact diag. application for the FQHE effect on a thin-torus. This can be mapped to a 1D problem on a ring which has both total momenta (P) and total center-of-mass conservation (X). In a ring the position (j), is actually ill defined, therefore I need to define X as a non-Hermitian operator $X = \sum_j e^{i 2\pi j/L} \psi^{\dagger}_x \psi_x$ instead. My questions are: ---------------------- 1. Could a non-Hermitian operator such as X, be given as a conserved quantum number to the exact/sparse diagonalization applications ? 2. For a ring geometry and when within an tag: may I use the site's name ("j") as though it is a variable which holds an integer denoting the position (I need this for the last definition of X). Thanks in advance, Zohar.
On Oct 28, 2010, at 16:54, "Zohar Ringel" <Zohar.Ringel@weizmann.ac.il> wrote:
Dear ALPS developers,
Some background on the problem I have: --------------------------------------------------- I wish to use the exact diag. application for the FQHE effect on a thin-torus. This can be mapped to a 1D problem on a ring which has both total momenta (P) and total center-of-mass conservation (X). In a ring the position (j), is actually ill defined, therefore I need to define X as a non-Hermitian operator $X = \sum_j e^{i 2\pi j/L} \psi^{\dagger}_x \psi_x$ instead.
My questions are: ---------------------- 1. Could a non-Hermitian operator such as X, be given as a conserved quantum number to the exact/sparse diagonalization applications ?
No, currently conserved quantum numbers are just diagonal quantities in the local site Hilbert spaces. This will thus not work.
2. For a ring geometry and when within an <SITEOPERATOR name="X" site="j"> tag: may I use the site's name ("j") as though it is a variable which holds an integer denoting the position (I need this for the last definition of X).
You can just use the variables x, y and z to denote the x, y and z coordinates of the sites. However you then need to make sure to define your lattice as inhomogeneous. Matthias
participants (2)
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Matthias Troyer
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Zohar Ringel