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MpDimensions

(redirected from Main.MpDimensions)

mp-dimensions prints the dimension of each symmetry sector of a given lattice.

usage: mp-dimensions <lattice>

Examples

Supposing six-site-hubbard.lattice is a lattice file for the SO(4) symmetric Hubbard model on 6 sites.

will print

Symmetry list is Q:SU(2),S:SU(2)
Symmetry Sector                            Dimension
            0,0                                   70
            0,1                                   84
            0,2                                   20
            0,3                                    1
        0.5,0.5                                  140
        0.5,1.5                                   64
        0.5,2.5                                    6
            1,0                                   84
            1,1                                   90
            1,2                                   15
        1.5,0.5                                   64
        1.5,1.5                                   20
            2,0                                   20
            2,1                                   15
        2.5,0.5                                    6
            3,0                                    1

Total: 700

This example shows nicely the effect of SU(2) symmetry. The symmetry sectors here represent multiplets of degree (2q+1)(2s+1). Multiply this by the dimension and sum over all subspaces to get the full dimension of the Hilbert space, which is 4^6 = 4096.

Notes

This program uses arbitrary-length integer arithmetic and never overflows.

The ordering of the quantum numbers is a bit weird for quantum numbers larger than 127.

The output gets very big for large lattices. There really needs to be some way to restrict the output to just one quantum number, or a narrow range.