• View
• Edit
• Rename
• History
• Print
• Backlinks

MpAuxMatrix

The mp-aux-matrix command constructs the auxiliary space representation of lattice operators, which are written to a file in a sparse-matrix format suitable for use in eg MATLAB.

Synopsis

mp-aux-matrix[options] -w <psi> -l <lattice> [-{p,t,f} <file>=<operator>] ...

Given the supplied infinite wavefunction and lattice file, the main arguments are a list of operators and output files, which can be either product MPOs, triangular MPOs, or finite operators.

The matrix elements of the operator are evaluated, and written into the file in sparse format of 4 columns: row, column, real, imag. It is also possible to use a polar format with the --polar option.

The numbering of the rows/columns is 1-based, and is in the order of density matrices, from largest to smallest. Because the matrices can be very big, it is often useful to just show a few of the matrix elements corresponding to the largest eigenvalues, which can be done with the --restrict option.

Options

--help

-w, '''--wavefunction

-l, '''--lattice

-p, --product file=operator

-t, --triangular file=operator

--restrict

--degree =0

'''polar

'''radians

Examples

1. Calculate the Hamiltonian matrix elements
   

   spinchain-u1 -o lat
   mp-idmrg-s3e -H lat:"H_J1" -m 10x100 -q 0 -u 2 --create -w psi
   mp-aux-matrix -w psi -l lat -t file="H_J1"
   cat file
   

2. As above but only output the 4x4 matrix corresponding to the largest density matrix eigenvalues
   mp-aux-matrix -w psi -l lat -t file="H_J1" --restrict 1,2,3,4
3. If we calculate the degree 1 component of the Hamiltonian, this is just the energy * identity matrix
   mp-aux-matrix -w psi -l lat -t file="H_J1" --degree 1

This command is very useful for calculating the matrix elements of SPT symmetry operators, so an example should be added.

Notes

For triangular operators, the toolkit chooses to fix the trace to be zero (strictly speaking, the trace weighted by the density matrix, so that {$\mathrm{Tr} A \rho = 0$}). This is a somewhat arbitrary choice, since this value is just a constant boundary term and could be taken to be anything, which amounts to a constant shift of the operator {$A \rightarrow A + xI$}.

Finite operators are not yet supported.

Currently this tool only constructs operators at the edge of the unit cell; other partitions are not yet supported.

See also

• mp-aux-algebra?