The mp-info command displays a wide variety of information about a wavefunction.
Synopsis
mp-info [options] <wavefunction>
When used with a wavefunction but no additional options, mp-info displays a short set of statistics about a wavefunction, including the type of wavefunction (finite, infinite, etc), the symmetry list, number of sites, attributes, and the most recent history log. Options can be used to display information such as the entropy or number of states at each partition (or some subset of partitions).
mp-info can also be used to display warranty and software license information.
Options
Here, a partition refers to a bond between two MPS matrices. The numbering starts at zero, which is the left-hand edge (for a finite wavefunction) or the unit cell edge (for an infinite wavefunction).
--help
show help message
-e, --entropy
List the entropy at each partition
-2, --base2
Implies --entropy; display the entropy in base 2, rather than the default base e
-s, --states
List the number of states at each partition
-a, --basis
List the basis at each partition (number of states in each quantum number sector)
-d, --density-matrix
Show the full density matrix / entanglement spectrum at each partition
--degen
Implies --density-matrix; for non-abelian symmetries, show multiplets as repeated eigenvalues
-l, --limit=N
Implies --density-matrix; only show the first N eigenvalues
-c, --casimir
Show the values of the casimir invariant operators of the symmetries at each partition, including the second moments {$(O-\langle O \rangle)^2$}
-b, --localbasis
List the local basis (physical basis) at each site of the wavefunction
-p, --partition=N
Show quantities only for partition N. Can be used more than once
--warranty
Display software warranty information
--copying
Display software distribution license conditions
--copying
Display software citation recommendations
Examples
- To display some general information about a wavefunction:
$ mp-info K1-alpha0.625.psi
Wavefunction is an InfiniteWavefunction in the left canonical basis.
Symmetry list = N:U(1)
Unit cell size = 26
Quantum number per unit cell = 4
Number of states = 597
Attributes:
Hamiltonian=lattice:H{alpha=0.6153846153846154,K=1}
LastEnergy=-8.9062170194985484
Last history entry:
Date: Wed, 06 Apr 2016 04:25:37 +1000
mp-idmrg-s3e -H "lattice:H{alpha=0.6153846153846154,K=1}" -m 400..600x100 -w K1-alpha0.625.psi
- To display the entropy at partitions 0 and 1 of a wavefunction:
$ mp-info -e -p 0 -p 1 K1-alpha0.625.psi
#left-size #right-size #entropy(base-e)
0 26 1.4372911100946
1 25 1.5024930232031
- To display the number of states in each symmetry sector at partition 1:
$ mp-info -a -p 1 K1-alpha0.625.psi
Basis at partition 1:
Basis has symmetry N:U(1), subspace size = 8, dimension = 544, degree = 544
N QuantumNumber Dimension
0 0 1
1 1 15
2 2 73
3 3 162
4 4 165
5 5 94
6 6 30
7 7 4
Note: the column N is the internal index of each subspace, it has no physical meaning and the ordering is arbitrary. In some circumstances it is possible to have more than one subspace with the same quantum number label.
- To display the reduced density matrix (entanglement spectrum) at partition 0, limited to the largest 20 eigenvalues:
$ mp-info -d --limit 20 -p 0 K1-alpha0.625.psi
#Reduced density matrix at partition (0,26) :
#Eigenvalue sum = 1.000000000000e+00
#von Neumann Entropy (base e) = 1.437291110095e+00
#Number #Eigenvalue #Degen #Weight #Energy #QuantumNumber
1 5.928201423608e-01 1 5.928201423608e-01 5.228642272361e-01 4
2 1.239673154979e-01 1 1.239673154979e-01 2.087737332816e+00 4
3 1.168820881692e-01 1 1.168820881692e-01 2.146589645776e+00 5
4 7.630549742846e-02 1 7.630549742846e-02 2.573010293111e+00 3
5 2.077160702277e-02 1 2.077160702277e-02 3.874168271782e+00 4
6 1.971973360759e-02 1 1.971973360759e-02 3.926135438642e+00 5
7 1.398284409998e-02 1 1.398284409998e-02 4.269924122240e+00 3
8 1.257695768917e-02 1 1.257695768917e-02 4.375888894066e+00 4
9 4.372353356221e-03 1 4.372353356221e-03 5.432453889376e+00 5
10 3.306855103951e-03 1 3.306855103951e-03 5.711757660895e+00 4
11 3.197362170190e-03 1 3.197362170190e-03 5.745429130932e+00 3
12 2.261534285691e-03 1 2.261534285691e-03 6.091711808564e+00 5
13 1.718156334484e-03 1 1.718156334484e-03 6.366503461607e+00 4
14 1.471113866580e-03 1 1.471113866580e-03 6.521735432758e+00 3
15 9.273368235416e-04 1 9.273368235416e-04 6.983193710452e+00 4
16 8.009338611585e-04 1 8.009338611585e-04 7.129732184644e+00 5
17 7.868953851359e-04 1 7.868953851359e-04 7.147415247054e+00 6
18 5.536601744628e-04 1 5.536601744628e-04 7.498959462923e+00 3
19 5.286368140162e-04 1 5.286368140162e-04 7.545208913845e+00 4
20 4.118440377230e-04 1 4.118440377230e-04 7.794865829499e+00 2
#20 out of 597 eigenvalues shown. Total degree = 20
The #Eigenvalue column is the eigenvalue of the reduced density matrix, with its non-abelian degeneracy in the #Degen column. For abelian symmetries, the #Degen is always 1. For non-abelian symmetries, this is the degree of the quantum number (irred rep). The #Weight is the product of the eigenvalue and its degeneracy. The sum of the weights will normally be equal to 1.0 (for a properly normalized wavefunction). The #Energy column is the entanglement energy of the eigenstate, equal to the negative natural log of the eigenvalue.
- Density matrix for an {$SU(2)$} symmetric example:
$ mp-info -d -p 0 psi
#Reduced density matrix at partition (0,2) :
#Eigenvalue sum = 1.000000000000e+00
#von Neumann Entropy (base e) = 1.193141690416e+00
#Number #Eigenvalue #Degen #Weight #Energy #QuantumNumber
1 6.394315357546e-01 1 6.394315357546e-01 4.471757227178e-01 0
2 1.086209260539e-01 3 3.258627781618e-01 2.219891200782e+00 1
3 8.077672390815e-03 3 2.423301717244e-02 4.818651518393e+00 1
4 5.533069746900e-03 1 5.533069746900e-03 5.197012509525e+00 0
5 8.586266864291e-04 3 2.575880059287e-03 7.060176321328e+00 1
6 3.146868315338e-04 3 9.440604946013e-04 8.063932599276e+00 1
7 2.101939455361e-04 5 1.050969727680e-03 8.467479903285e+00 2
8 1.997687568267e-04 1 1.997687568267e-04 8.518350076216e+00 0
9 2.983486582185e-05 3 8.950459746554e-05 1.041983285434e+01 1
10 1.541826462455e-05 1 1.541826462455e-05 1.107995773672e+01 0
11 6.775060418589e-06 5 3.387530209294e-05 1.190226227337e+01 2
12 4.577508515517e-06 3 1.373252554655e-05 1.229435570010e+01 1
13 2.341338393720e-06 3 7.024015181161e-06 1.296478782897e+01 1
14 2.266776213374e-06 1 2.266776213374e-06 1.299715190619e+01 0
15 1.286862252805e-06 3 3.860586758416e-06 1.356330366476e+01 1
16 3.185784191322e-07 3 9.557352573965e-07 1.495939717832e+01 1
17 3.048153074609e-07 5 1.524076537304e-06 1.500355979307e+01 2
18 1.210570516553e-07 3 3.631711549659e-07 1.592700390119e+01 1
19 9.000846849760e-08 1 9.000846849760e-08 1.622336207662e+01 0
20 6.101332375205e-08 5 3.050666187603e-07 1.661217357446e+01 2
#20 out of 20 eigenvalues shown. Total degree = 56
This is for a spin-1/2 Heisenberg chain with m=20 states kept. The #Degen column is the number of states in each multipliet, equal to {$2j+1$} for total spin quantum number {$j$} (the #QuantumNumber column).
- Order parameter fluctuations
The Casimir invariants, and their moments, are useful for calculating the stiffness via order parameter fluctuations. See HOWTO.Stiffness?
See also
