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Commit 90a541e5 authored by Isidora Araya's avatar Isidora Araya
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add instructions on how to save and load qsymm models

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docs/source/tutorial/basics.rst
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......@@ -209,3 +209,24 @@ It is exactly the Hamiltonian family we started with.
For more detailed examples see :ref:`tutorial_kdotp_generator`, :ref:`tutorial_bloch_generator`
and :ref:`tutorial_kekule`.
Saving and loading Qsymm models
-------------------------------------------------
We can save and load Qsymm models.
To save we do:
.. jupyter-execute::
H2D_str = str(H2D.tosympy(nsimplify=True))
file = open("H2D.txt", "w")
file.write(H2D_str)
file.close()
To load we do:
.. jupyter-execute::
f = open('H2D.txt','r').read()
loaded_H2D = qsymm.Model(sympy.parsing.sympy_parser.parse_expr(f), momenta=['k_x', 'k_z'])
qsymm/json_serialization/convert_func.py deleted 100644 → 0
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import numpy as np
import sympy
import re
import json
from astropy.utils.misc import JsonCustomEncoder
import qsymm
from icecream import ic
def bloch_model_to_json(model, name):
name = name + '.json'
model_dict = {str(key) : model[key].tolist() for key in model.keys()}
with open(name, 'w') as f:
json.dump(model_dict, f, cls = JsonCustomEncoder)
def bloch_model_from_json(name):
with open("json_models/" + name + ".json", "r") as f:
model = json.load(f, cls=JsonCustomDecoderExp)
return qsymm.Model(model, momenta=["k_x", "k_y"])
class JsonCustomDecoderExp(json.JSONDecoder):
"""
A decoder function tailored specifically to our purposes: take a dictionary of strings, output a dictionary
of symbolic keys (Mul types etc.) and arrays.
"""
def __init__(self, *args, **kwargs):
json.JSONDecoder.__init__(self, object_hook=self.object_hook, *args, **kwargs)
def object_hook(self, obj):
new_dict = dict()
for key in obj.keys():
# back-convert the key from string to symbols
symbolic = []
# find exponents, works for arbitrary number of exponents
exp_full = re.findall('\*?e\*\*\(-?I\*k_\w\)\*?', key) # gives list with exponential terms in key
if exp_full:
coef = key
for exp in exp_full:
coef = coef.replace(exp, '') # constant coefficient
exp_power_pl = re.findall('\*?e\*\*\(I\*(k_\w)\)\*?', key) # gives list of positive exponents
exp_power_mn = re.findall('\*?e\*\*\(-I\*(k_\w)\)\*?', key) # gives list of negative exponents
if len(exp_power_pl)>=1:
sym_exp_pls = []
for exp in exp_power_pl:
sym_exp_pls.append(sympy.Pow(sympy.Symbol('e'), sympy.I*sympy.Symbol(exp)))
if len(exp_power_mn)==0: # no negative powers
symbolic_key = sympy.Mul(*sym_exp_pls, sympy.Symbol(coef))
if len(exp_power_mn)>=1:
sym_exp_mns = []
for exp in exp_power_mn:
sym_exp_mns.append(sympy.Pow(sympy.Symbol('e'), -sympy.I*sympy.Symbol(exp)))
if len(exp_power_pl)==0: # no positive powers
symbolic_key = sympy.Mul(*sym_exp_mns, sympy.Symbol(coef))
else: # both positive and negative powers
symbolic_key = sympy.Mul(*sym_exp_mns, *sym_exp_pls, sympy.Symbol(coef))
else:
symbolic_key = sympy.Symbol(key)
assert str(key)==str(symbolic_key) # make sure converter works
array = []
for line in obj[key]:
lineski = []
for entry in line:
lineski.append(entry[0] + 1j * entry[1])
array.append(lineski)
new_dict[symbolic_key] = np.array(array)
return new_dict
qsymm/json_serialization/minimal_model.ipynb deleted 100644 → 0
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%% Cell type:code id:ec96970a-359f-4e6f-b2d9-529749253dab tags:
``` python
import numpy as np
import tinyarray
import qsymm
import sympy
from sympy import Matrix
import string
from convert_func import bloch_model_from_json, bloch_model_to_json
```
%% Cell type:code id:d7832d0c-1b99-47aa-9a40-00091eda980e tags:
``` python
sigma_x = tinyarray.array([[0, 1], [1, 0]])
sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
sigma_z = tinyarray.array([[1, 0], [0, -1]])
#create qsymm model
ham = " cos(k_x) * sigma_z + sin(k_y) * eye(2) "
H = qsymm.Model(ham, momenta=["k_x", "k_y"])
H.tosympy()
```
%% Output
$\displaystyle \left[\begin{matrix}0.5 e^{i k_{x}} - 0.5 i e^{i k_{y}} + 0.5 i e^{- i k_{y}} + 0.5 e^{- i k_{x}} & 0\\0 & - 0.5 e^{i k_{x}} - 0.5 i e^{i k_{y}} + 0.5 i e^{- i k_{y}} - 0.5 e^{- i k_{x}}\end{matrix}\right]$
Matrix([
[0.5*e**(I*k_x) - 0.5*I*e**(I*k_y) + 0.5*I*e**(-I*k_y) + 0.5*e**(-I*k_x), 0],
[ 0, -0.5*e**(I*k_x) - 0.5*I*e**(I*k_y) + 0.5*I*e**(-I*k_y) - 0.5*e**(-I*k_x)]])
%% Cell type:code id:309fb778-7db3-4a02-a163-ab6479aa7711 tags:
``` python
#find symmetries
candidates = qsymm.groups.square()
discrete_symm, continuous_symm = qsymm.symmetries(H, candidates)
print(len(discrete_symm), len(continuous_symm))
abcd_sympy = list(sympy.symbols('a:z'))
abcd_list = list(string.ascii_lowercase)
del abcd_sympy[4]
del abcd_list[4]
norbs = [('A', 2)] # A atom per unit cell, 4 orbitals each
hopping_vectors = [('A', 'A', [0, 1]), ('A', 'A', [1, 0])]
#find all temrs compatible with 1 specific symmetry
family= qsymm.bloch_family(hopping_vectors, [discrete_symm[1]], norbs)
#add all the terms compatible with the symmetry
H = (H + sum([symbol * term for symbol, term in zip(abcd_sympy[3:], family)]))
H.tosympy(nsimplify=True)
```
%% Output
8 1
$\displaystyle \left[\begin{matrix}d + e^{i k_{x}} i + \frac{e^{i k_{x}}}{2} + e^{i k_{y}} m + i e^{i k_{y}} q - \frac{i e^{i k_{y}}}{2} + e^{- i k_{y}} m - i e^{- i k_{y}} q + \frac{i e^{- i k_{y}}}{2} + e^{- i k_{x}} i + \frac{e^{- i k_{x}}}{2} & e^{i k_{x}} j + i e^{i k_{x}} l + e^{i k_{y}} n + i e^{i k_{y}} r + f + i h + e^{- i k_{y}} o - i e^{- i k_{y}} s + e^{- i k_{x}} j + i e^{- i k_{x}} l\\e^{i k_{x}} j - i e^{i k_{x}} l + e^{i k_{y}} o + i e^{i k_{y}} s + f - i h + e^{- i k_{y}} n - i e^{- i k_{y}} r + e^{- i k_{x}} j - i e^{- i k_{x}} l & e^{i k_{x}} k - \frac{e^{i k_{x}}}{2} + e^{i k_{y}} p + i e^{i k_{y}} t - \frac{i e^{i k_{y}}}{2} + g + e^{- i k_{y}} p - i e^{- i k_{y}} t + \frac{i e^{- i k_{y}}}{2} + e^{- i k_{x}} k - \frac{e^{- i k_{x}}}{2}\end{matrix}\right]$
Matrix([
[d + e**(I*k_x)*i + e**(I*k_x)/2 + e**(I*k_y)*m + I*e**(I*k_y)*q - I*e**(I*k_y)/2 + e**(-I*k_y)*m - I*e**(-I*k_y)*q + I*e**(-I*k_y)/2 + e**(-I*k_x)*i + e**(-I*k_x)/2, e**(I*k_x)*j + I*e**(I*k_x)*l + e**(I*k_y)*n + I*e**(I*k_y)*r + f + I*h + e**(-I*k_y)*o - I*e**(-I*k_y)*s + e**(-I*k_x)*j + I*e**(-I*k_x)*l],
[ e**(I*k_x)*j - I*e**(I*k_x)*l + e**(I*k_y)*o + I*e**(I*k_y)*s + f - I*h + e**(-I*k_y)*n - I*e**(-I*k_y)*r + e**(-I*k_x)*j - I*e**(-I*k_x)*l, e**(I*k_x)*k - e**(I*k_x)/2 + e**(I*k_y)*p + I*e**(I*k_y)*t - I*e**(I*k_y)/2 + g + e**(-I*k_y)*p - I*e**(-I*k_y)*t + I*e**(-I*k_y)/2 + e**(-I*k_x)*k - e**(-I*k_x)/2]])
%% Cell type:code id:387f8212-1861-4875-8fc5-798cb5d83220 tags:
``` python
bloch_model_to_json(H, 'model')
```
%% Cell type:code id:de61fbf0-f6a6-43db-b32c-300e408fcbd3 tags:
``` python
```
%% Cell type:code id:f5cb9c98-cc14-448d-8a03-41df556ce3d2 tags:
``` python
```
qsymm/json_serialization/model.json deleted 100644 → 0
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{"e**(-I*k_x)": [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [-0.5, 0.0]]], "e**(-I*k_y)": [[[0.0, 0.5], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.5]]], "e**(I*k_x)": [[[0.5, 0.0], [0.0, 0.0]], [[0.0, 0.0], [-0.5, 0.0]]], "e**(I*k_y)": [[[0.0, -0.5], [0.0, 0.0]], [[0.0, 0.0], [0.0, -0.5]]], "e**(-I*k_x)*l": [[[-0.0, 0.0], [0.0, 1.0]], [[0.0, -1.0], [-0.0, 0.0]]], "e**(-I*k_x)*j": [[[0.0, 0.0], [1.0, 0.0]], [[1.0, 0.0], [0.0, 0.0]]], "e**(I*k_y)*s": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 1.0], [0.0, 0.0]]], "e**(-I*k_y)*o": [[[0.0, 0.0], [1.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(-I*k_y)*t": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, -1.0]]], "e**(-I*k_y)*m": [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(I*k_y)*o": [[[0.0, 0.0], [0.0, 0.0]], [[1.0, 0.0], [0.0, 0.0]]], "e**(I*k_y)*t": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 1.0]]], "e**(I*k_y)*m": [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(-I*k_y)*r": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, -1.0], [0.0, 0.0]]], "e**(-I*k_y)*n": [[[0.0, 0.0], [0.0, 0.0]], [[1.0, 0.0], [0.0, 0.0]]], "e**(-I*k_x)*i": [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(I*k_x)*j": [[[0.0, 0.0], [1.0, 0.0]], [[1.0, 0.0], [0.0, 0.0]]], "e**(I*k_x)*l": [[[-0.0, 0.0], [0.0, 1.0]], [[0.0, -1.0], [-0.0, 0.0]]], "e**(-I*k_x)*k": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [1.0, 0.0]]], "e**(-I*k_y)*p": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [1.0, 0.0]]], "d": [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "f": [[[0.0, 0.0], [1.0, 0.0]], [[1.0, 0.0], [0.0, 0.0]]], "e**(I*k_y)*n": [[[0.0, 0.0], [1.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "h": [[[-0.0, 0.0], [0.0, 1.0]], [[0.0, -1.0], [-0.0, 0.0]]], "e**(I*k_y)*p": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [1.0, 0.0]]], "e**(-I*k_y)*q": [[[0.0, -1.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(I*k_y)*r": [[[0.0, 0.0], [0.0, 1.0]], [[0.0, 0.0], [0.0, 0.0]]], "g": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [1.0, 0.0]]], "e**(I*k_y)*q": [[[0.0, 1.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(I*k_x)*i": [[[1.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]], "e**(I*k_x)*k": [[[0.0, 0.0], [0.0, 0.0]], [[0.0, 0.0], [1.0, 0.0]]], "e**(-I*k_y)*s": [[[0.0, 0.0], [0.0, -1.0]], [[0.0, 0.0], [0.0, 0.0]]]}
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