Module spinparser.obs
Collection of functions to import data from ".obs" files generated by SpinParser. Provides convenient access to lattice geometry, spin correlations, and the spin structure factor.
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"""
Collection of functions to import data from ".obs" files generated by SpinParser.
Provides convenient access to lattice geometry, spin correlations, and the spin structure factor.
"""
import warnings
import h5py
import numpy as np
def _getObsAttributes(obsIdentifier):
"""
For a given obsfile identifier, return a list of all contained datasets.
Args:
obsIdentifier (str): obsfile identifier (hdf5 dataset name).
Returns:
list[str]: List of data contained on the obsfile identifier.
"""
if (obsIdentifier == "TRICorDD"):
return [ "CorrelationDD", "LatticeData" ]
elif (obsIdentifier == "TRICorXX"):
return [ "CorrelationXX", "LatticeData" ]
elif (obsIdentifier == "TRICorXY"):
return [ "CorrelationXY", "LatticeData" ]
elif (obsIdentifier == "TRICorXZ"):
return [ "CorrelationXZ", "LatticeData" ]
elif (obsIdentifier == "TRICorYX"):
return [ "CorrelationYX", "LatticeData" ]
elif (obsIdentifier == "TRICorYY"):
return [ "CorrelationYY", "LatticeData" ]
elif (obsIdentifier == "TRICorYZ"):
return [ "CorrelationYZ", "LatticeData" ]
elif (obsIdentifier == "TRICorZX"):
return [ "CorrelationZX", "LatticeData" ]
elif (obsIdentifier == "TRICorZY"):
return [ "CorrelationZY", "LatticeData" ]
elif (obsIdentifier == "TRICorZZ"):
return [ "CorrelationZZ", "LatticeData" ]
elif (obsIdentifier == "XYZCorDD"):
return [ "CorrelationDD", "LatticeData" ]
elif (obsIdentifier == "XYZCorXX"):
return [ "CorrelationXX", "LatticeData" ]
elif (obsIdentifier == "XYZCorYY"):
return [ "CorrelationYY", "LatticeData" ]
elif (obsIdentifier == "XYZCorZZ"):
return [ "CorrelationZZ", "LatticeData" ]
elif (obsIdentifier == "SU2CorDD"):
return [ "CorrelationDD", "LatticeData" ]
elif (obsIdentifier == "SU2CorZZ"):
return [ "CorrelationXX", "CorrelationYY", "CorrelationZZ", "LatticeData" ]
else:
raise Exception("Unknown observable identifier %s" % obsIdentifier)
def getLatticeBasis(obsfile):
"""
Return the lattice basis for the lattice graph used in the calculation of the specified obsfile.
Args:
obsfile (str): Path to the obsfile.
Returns:
numpy.ndarray: Array of coordinates of lattice basis sites. For an N-site basis, the return array has shape (N,3), with the second dimension storing the x, y, and z components of the position vector.
"""
with h5py.File(obsfile, "r") as file:
for obsIdentifier in file.keys():
if "LatticeData" in _getObsAttributes(obsIdentifier):
return file[obsIdentifier+"/meta/basis"][()]
raise Exception("Observable file does not contain lattice basis information.")
def getLatticePrimitives(obsfile):
"""
Return the primitive lattice vectors for the lattice graph used in the calculation of the specified obsfile.
Args:
obsfile (str): Path to the obsfile.
Returns:
numpy.ndarray: Array of primitive lattice vectors. The return array has shape (3,3), with the first dimension enumerating the primitives, and the second dimension storing the x, y, and z components of the primitive.
"""
with h5py.File(obsfile, "r") as file:
for obsIdentifier in file.keys():
if ("LatticeData" in _getObsAttributes(obsIdentifier)):
return file[obsIdentifier+"/meta/latticeVectors"][()]
raise Exception("Observable file does not contain primitive lattice vector information.")
def _getCutoffValues(obsfile, identifier, verbose=True):
with h5py.File(obsfile, "r") as file:
try:
measurements = list(file[identifier+"/data"].keys())
measurements = sorted(measurements, key=lambda x:int(x.split("_")[1]))
cutoffs = np.array([ file[identifier+"/data/"+m].attrs["cutoff"][0] for m in measurements ])
return {"data":cutoffs, "measurements":measurements} if verbose else cutoffs
except:
raise Exception("Observable file does not contain cutoff information under the given observable identifier.")
def getLatticeSites(obsfile, reference=0, verbose=True):
"""
Get a list of all lattice sites within truncation range of a specified reference site.
Args:
obsfile (str): Path to the obsfile.
reference (Union[int,list,numpy.array],optional): Reference site. Can be either an integer `n` which refers to the n-th basis site, or a three-component list or numpy.array which specifies the real-space position of a basis site. Defaults to 0.
verbose (bool, optional): Defines whether the output should be verbose. Defaults to True.
Returns:
Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,3) where N is the number of sites within truncation range, and the second dimension stores the x, y, and z components of the lattice site position.
If the output is verbose, return a dict with keys `data`, containing the nonverbose data, and `reference`, which contains the real-space position of the specified reference site.
"""
#parse argument `reference`
if type(reference) == int and reference < len(getLatticeBasis(obsfile)): reference = getLatticeBasis(obsfile)[reference,:]
elif type(reference) == list: reference = np.array(reference)
if not (reference.ndim == 1 and len(reference) == 3): raise Exception("Invalid argument type: reference")
referenceList = getLatticeBasis(obsfile)
distanceTable = [np.linalg.norm(x-reference) for x in referenceList]
if np.min(distanceTable) > 1e-3: raise Exception("Specified reference site does not match any basis site. Try higher precision or select from getLatticeBasis().")
referenceFilter = np.argmin(distanceTable)
#read data
out = None
with h5py.File(obsfile, "r") as file:
for obsIdentifier in file.keys():
if ("LatticeData" in _getObsAttributes(obsIdentifier)):
raw = file[obsIdentifier+"/meta/sites"][()]
out = {"data":raw[referenceFilter,:], "reference":referenceList[referenceFilter,:]}
break
#return data
if not out: raise Exception("Observable file does not contain lattice site information.")
return out if verbose else out["data"]
def getCorrelation(obsfile, cutoff="all", site="all", reference=0, component="all", verbose=True):
"""
Obtain correlation data from an observables file.
Args:
obsfile (str): Path to the obsfile.
cutoff (Union[float,list,numpy.array,str], optional): Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all".
site (Union[list,numpy.array,str], optional): Lattice sites at which to retrieve data. Can be a list of x,y,z real-space coordinates of a site, a list of multiple sites, or "all". Defaults to "all".
reference (Union[int,list,numpy.array], optional): Reference site for the correlation measurement. Can be either an integer `n` which refers to the `n`-th basis site, or a three-component list or numpy.array that specifies the real-space position of a basis site. Defaults to 0.
component (str, optional): Spin component of the correlation function to retrieve. Can be "XX", "XY", "XZ", "YX", ..., "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all".
verbose (bool, optional): Defines whether the output should be verbose. Defaults to True.
Returns:
Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of sites selected.
If the output is verbose, return a dict with keys `data` (contains the nonverbose data), `cutoff` (contains the selected cutoff values), `site` (contains the selected lattice sites), and `reference` (contains the real-space position of the specified reference site).
"""
if component == "all":
out = getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=True, component="XX")
out["data"] += getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=False, component="YY")
out["data"] += getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=False, component="ZZ")
else:
out = None
with h5py.File(obsfile, "r") as file:
for obsIdentifier in file.keys():
if ("Correlation"+component in _getObsAttributes(obsIdentifier)):
#parse argument `reference`
referenceList = getLatticeBasis(obsfile)
if type(reference) == int and reference < len(referenceList): reference = referenceList[reference,:]
elif type(reference) == list: reference = np.array(reference)
if not (reference.ndim == 1 and len(reference) == 3): raise Exception("Invalid argument type: reference")
distanceTable = [np.linalg.norm(x-reference) for x in referenceList]
referenceFilter = int(np.argmin(distanceTable))
if np.min(distanceTable) > 1e-3: warnings.warn("Specified reference site %s does not match any basis site. Using closest site: %s" % (reference, referenceList[referenceFilter]))
#parse argument `site`
siteList = getLatticeSites(obsfile, reference=referenceFilter, verbose=False)
if type(site) == str and site == "all": site = siteList
elif type(site) == list: site = np.array(site)
if site.ndim == 1: site = np.reshape(site, (1,len(site)))
if not (site.ndim == 2 and site.shape[1] == 3): raise Exception("Invalid argument type: site")
siteFilter = []
for i in range(len(site)):
distanceTable = [np.linalg.norm(x-site[i]) for x in siteList]
siteFilter.append(np.argmin(distanceTable))
if np.min(distanceTable) > 1e-3: warnings.warn("Specified lattice site %s does not match any site in the lattice. Using closest site: %s" % (site[i], siteList[siteFilter[-1]]))
#parse argument `cutoff`
cutoffValues = _getCutoffValues(obsfile, obsIdentifier)
cutoffList = cutoffValues["data"]
measurementList = cutoffValues["measurements"]
if type(cutoff) == str and cutoff == "all": cutoff = cutoffList
elif type(cutoff) == float: cutoff = np.array([cutoff])
elif type(cutoff) == list: cutoff = np.array(cutoff)
if not (cutoff.ndim == 1 and len(cutoff) > 0): raise Exception("Invalid argument type: cutoff")
cutoffFilter = []
cutoffFilterMeasurements = []
for i in range(len(cutoff)):
distanceTable = [abs(x-cutoff[i]) for x in cutoffList]
cutoffFilter.append(np.argmin(distanceTable))
cutoffFilterMeasurements.append(measurementList[np.argmin(distanceTable)])
if np.min(distanceTable) > 1e-3: warnings.warn("Specified cutoff value %f does not match any recorded cutoff. Using closest value: %f" % (cutoff[i], cutoffList[cutoffFilter[-1]]))
#read data
data = np.ndarray((0,len(siteFilter)), dtype=np.float32)
for i in range(len(cutoffFilter)):
dset = file[obsIdentifier+"/data/"+cutoffFilterMeasurements[i]+"/data"][()]
dset = np.reshape(dset[referenceFilter, siteFilter], (1,len(siteFilter)))
data = np.concatenate((data, dset), axis=0)
out = {"data":data, "cutoff":cutoffList[cutoffFilter], "site":siteList[siteFilter], "reference":referenceList[referenceFilter]}
break
#return data
if not out: raise Exception("Observable file does not contain specificed correlation information.")
return out if verbose else out["data"]
def getStructureFactor(obsfile, momentum, cutoff="all", component="all", verbose=True):
r"""
Calculate the spin structure factor from the spin correlations stored in an observable file.
The structure factor is defined as the Fourier transform of the real-space correlations \( \chi^{\mu\nu}_{ij} \), normalized by the number of lattice sites, \( N_L \).
See the SpinParser documentation for information on the real-space correlations.
The expression for the structure factor is given by
\[ \chi^{\mu\nu}(\mathbf{k})=\frac{1}{N_L}\sum_{i,j} \exp[i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j)] \chi^{\mu\nu}_{ij} \]
Args:
obsfile (str): Path to the obsfile.
momentum (Union[list,numpy.array]): Momentum points at which to compute the structure factor. Can be a one-dimensional list or array of three kx,ky,kz coordinates, or a two-dimensional list or array of multiple momentum points.
cutoff (Union[float,list,numpy.array,str], optional): Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all".
component (str, optional): Spin component of the structure factor to retrieve. Can be "XX", "XY", "XZ", "YX", ..., "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all".
verbose (bool, optional): Defines whether the output should be verbose. Defaults to True.
Returns:
Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of momentum points specified.
If the output is verbose, return a dict with keys `data` (contains the nonverbose data), `cutoff` (contains the selected cutoff values), and `momentum` (momentum points).
"""
#parse argument `momentum`
if type(momentum) == list: momentum = np.array(momentum)
if momentum.ndim == 1: momentum = np.reshape(momentum, (1,len(momentum)))
if not (momentum.ndim == 2 and momentum.shape[1] == 3): raise Exception("Invalid argument type: momentum")
#get correlation
basis = getLatticeBasis(obsfile)
cutoffList = getCorrelation(obsfile, cutoff=cutoff, site="all", reference=0, component=component, verbose=True)["cutoff"]
data = np.zeros((len(cutoffList),len(momentum)), dtype=np.float32)
for i in range(len(basis)):
raw = getCorrelation(obsfile, cutoff=cutoff, site="all", reference=i, component=component, verbose=True)
for i_c in range(len(raw["cutoff"])):
for i_k in range(len(momentum)):
for i_s in range(len(raw["site"])):
data[i_c,i_k] += raw["data"][i_c,i_s] * np.cos(np.dot(momentum[i_k], raw["site"][i_s] - raw["reference"]))
data /= len(basis)
out = {"data":data, "cutoff":cutoffList, "momentum":momentum}
#return data
return out if verbose else out["data"]Functions
def getCorrelation(obsfile, cutoff='all', site='all', reference=0, component='all', verbose=True)-
Obtain correlation data from an observables file.
Args
obsfile:str- Path to the obsfile.
cutoff:Union[float,list,numpy.array,str], optional- Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all".
site:Union[list,numpy.array,str], optional- Lattice sites at which to retrieve data. Can be a list of x,y,z real-space coordinates of a site, a list of multiple sites, or "all". Defaults to "all".
reference:Union[int,list,numpy.array], optional- Reference site for the correlation measurement. Can be either an integer
nwhich refers to then-th basis site, or a three-component list or numpy.array that specifies the real-space position of a basis site. Defaults to 0. component:str, optional- Spin component of the correlation function to retrieve. Can be "XX", "XY", "XZ", "YX", …, "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all".
verbose:bool, optional- Defines whether the output should be verbose. Defaults to True.
Returns
Union[dict,numpy.ndarray]- If
verbose==False, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of sites selected. If the output is verbose, return a dict with keysdata(contains the nonverbose data),cutoff(contains the selected cutoff values),site(contains the selected lattice sites), andreference(contains the real-space position of the specified reference site).
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def getCorrelation(obsfile, cutoff="all", site="all", reference=0, component="all", verbose=True): """ Obtain correlation data from an observables file. Args: obsfile (str): Path to the obsfile. cutoff (Union[float,list,numpy.array,str], optional): Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all". site (Union[list,numpy.array,str], optional): Lattice sites at which to retrieve data. Can be a list of x,y,z real-space coordinates of a site, a list of multiple sites, or "all". Defaults to "all". reference (Union[int,list,numpy.array], optional): Reference site for the correlation measurement. Can be either an integer `n` which refers to the `n`-th basis site, or a three-component list or numpy.array that specifies the real-space position of a basis site. Defaults to 0. component (str, optional): Spin component of the correlation function to retrieve. Can be "XX", "XY", "XZ", "YX", ..., "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all". verbose (bool, optional): Defines whether the output should be verbose. Defaults to True. Returns: Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of sites selected. If the output is verbose, return a dict with keys `data` (contains the nonverbose data), `cutoff` (contains the selected cutoff values), `site` (contains the selected lattice sites), and `reference` (contains the real-space position of the specified reference site). """ if component == "all": out = getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=True, component="XX") out["data"] += getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=False, component="YY") out["data"] += getCorrelation(obsfile, cutoff=cutoff, site=site, reference=reference, verbose=False, component="ZZ") else: out = None with h5py.File(obsfile, "r") as file: for obsIdentifier in file.keys(): if ("Correlation"+component in _getObsAttributes(obsIdentifier)): #parse argument `reference` referenceList = getLatticeBasis(obsfile) if type(reference) == int and reference < len(referenceList): reference = referenceList[reference,:] elif type(reference) == list: reference = np.array(reference) if not (reference.ndim == 1 and len(reference) == 3): raise Exception("Invalid argument type: reference") distanceTable = [np.linalg.norm(x-reference) for x in referenceList] referenceFilter = int(np.argmin(distanceTable)) if np.min(distanceTable) > 1e-3: warnings.warn("Specified reference site %s does not match any basis site. Using closest site: %s" % (reference, referenceList[referenceFilter])) #parse argument `site` siteList = getLatticeSites(obsfile, reference=referenceFilter, verbose=False) if type(site) == str and site == "all": site = siteList elif type(site) == list: site = np.array(site) if site.ndim == 1: site = np.reshape(site, (1,len(site))) if not (site.ndim == 2 and site.shape[1] == 3): raise Exception("Invalid argument type: site") siteFilter = [] for i in range(len(site)): distanceTable = [np.linalg.norm(x-site[i]) for x in siteList] siteFilter.append(np.argmin(distanceTable)) if np.min(distanceTable) > 1e-3: warnings.warn("Specified lattice site %s does not match any site in the lattice. Using closest site: %s" % (site[i], siteList[siteFilter[-1]])) #parse argument `cutoff` cutoffValues = _getCutoffValues(obsfile, obsIdentifier) cutoffList = cutoffValues["data"] measurementList = cutoffValues["measurements"] if type(cutoff) == str and cutoff == "all": cutoff = cutoffList elif type(cutoff) == float: cutoff = np.array([cutoff]) elif type(cutoff) == list: cutoff = np.array(cutoff) if not (cutoff.ndim == 1 and len(cutoff) > 0): raise Exception("Invalid argument type: cutoff") cutoffFilter = [] cutoffFilterMeasurements = [] for i in range(len(cutoff)): distanceTable = [abs(x-cutoff[i]) for x in cutoffList] cutoffFilter.append(np.argmin(distanceTable)) cutoffFilterMeasurements.append(measurementList[np.argmin(distanceTable)]) if np.min(distanceTable) > 1e-3: warnings.warn("Specified cutoff value %f does not match any recorded cutoff. Using closest value: %f" % (cutoff[i], cutoffList[cutoffFilter[-1]])) #read data data = np.ndarray((0,len(siteFilter)), dtype=np.float32) for i in range(len(cutoffFilter)): dset = file[obsIdentifier+"/data/"+cutoffFilterMeasurements[i]+"/data"][()] dset = np.reshape(dset[referenceFilter, siteFilter], (1,len(siteFilter))) data = np.concatenate((data, dset), axis=0) out = {"data":data, "cutoff":cutoffList[cutoffFilter], "site":siteList[siteFilter], "reference":referenceList[referenceFilter]} break #return data if not out: raise Exception("Observable file does not contain specificed correlation information.") return out if verbose else out["data"] def getLatticeBasis(obsfile)-
Return the lattice basis for the lattice graph used in the calculation of the specified obsfile.
Args
obsfile:str- Path to the obsfile.
Returns
numpy.ndarray- Array of coordinates of lattice basis sites. For an N-site basis, the return array has shape (N,3), with the second dimension storing the x, y, and z components of the position vector.
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def getLatticeBasis(obsfile): """ Return the lattice basis for the lattice graph used in the calculation of the specified obsfile. Args: obsfile (str): Path to the obsfile. Returns: numpy.ndarray: Array of coordinates of lattice basis sites. For an N-site basis, the return array has shape (N,3), with the second dimension storing the x, y, and z components of the position vector. """ with h5py.File(obsfile, "r") as file: for obsIdentifier in file.keys(): if "LatticeData" in _getObsAttributes(obsIdentifier): return file[obsIdentifier+"/meta/basis"][()] raise Exception("Observable file does not contain lattice basis information.") def getLatticePrimitives(obsfile)-
Return the primitive lattice vectors for the lattice graph used in the calculation of the specified obsfile.
Args
obsfile:str- Path to the obsfile.
Returns
numpy.ndarray- Array of primitive lattice vectors. The return array has shape (3,3), with the first dimension enumerating the primitives, and the second dimension storing the x, y, and z components of the primitive.
Expand source code
def getLatticePrimitives(obsfile): """ Return the primitive lattice vectors for the lattice graph used in the calculation of the specified obsfile. Args: obsfile (str): Path to the obsfile. Returns: numpy.ndarray: Array of primitive lattice vectors. The return array has shape (3,3), with the first dimension enumerating the primitives, and the second dimension storing the x, y, and z components of the primitive. """ with h5py.File(obsfile, "r") as file: for obsIdentifier in file.keys(): if ("LatticeData" in _getObsAttributes(obsIdentifier)): return file[obsIdentifier+"/meta/latticeVectors"][()] raise Exception("Observable file does not contain primitive lattice vector information.") def getLatticeSites(obsfile, reference=0, verbose=True)-
Get a list of all lattice sites within truncation range of a specified reference site.
Args
obsfile:str- Path to the obsfile.
reference:Union[int,list,numpy.array],optional- Reference site. Can be either an integer
nwhich refers to the n-th basis site, or a three-component list or numpy.array which specifies the real-space position of a basis site. Defaults to 0. verbose:bool, optional- Defines whether the output should be verbose. Defaults to True.
Returns
Union[dict,numpy.ndarray]- If
verbose==False, return an array of shape (N,3) where N is the number of sites within truncation range, and the second dimension stores the x, y, and z components of the lattice site position. If the output is verbose, return a dict with keysdata, containing the nonverbose data, andreference, which contains the real-space position of the specified reference site.
Expand source code
def getLatticeSites(obsfile, reference=0, verbose=True): """ Get a list of all lattice sites within truncation range of a specified reference site. Args: obsfile (str): Path to the obsfile. reference (Union[int,list,numpy.array],optional): Reference site. Can be either an integer `n` which refers to the n-th basis site, or a three-component list or numpy.array which specifies the real-space position of a basis site. Defaults to 0. verbose (bool, optional): Defines whether the output should be verbose. Defaults to True. Returns: Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,3) where N is the number of sites within truncation range, and the second dimension stores the x, y, and z components of the lattice site position. If the output is verbose, return a dict with keys `data`, containing the nonverbose data, and `reference`, which contains the real-space position of the specified reference site. """ #parse argument `reference` if type(reference) == int and reference < len(getLatticeBasis(obsfile)): reference = getLatticeBasis(obsfile)[reference,:] elif type(reference) == list: reference = np.array(reference) if not (reference.ndim == 1 and len(reference) == 3): raise Exception("Invalid argument type: reference") referenceList = getLatticeBasis(obsfile) distanceTable = [np.linalg.norm(x-reference) for x in referenceList] if np.min(distanceTable) > 1e-3: raise Exception("Specified reference site does not match any basis site. Try higher precision or select from getLatticeBasis().") referenceFilter = np.argmin(distanceTable) #read data out = None with h5py.File(obsfile, "r") as file: for obsIdentifier in file.keys(): if ("LatticeData" in _getObsAttributes(obsIdentifier)): raw = file[obsIdentifier+"/meta/sites"][()] out = {"data":raw[referenceFilter,:], "reference":referenceList[referenceFilter,:]} break #return data if not out: raise Exception("Observable file does not contain lattice site information.") return out if verbose else out["data"] def getStructureFactor(obsfile, momentum, cutoff='all', component='all', verbose=True)-
Calculate the spin structure factor from the spin correlations stored in an observable file. The structure factor is defined as the Fourier transform of the real-space correlations \chi^{\mu\nu}_{ij} , normalized by the number of lattice sites, N_L . See the SpinParser documentation for information on the real-space correlations. The expression for the structure factor is given by \chi^{\mu\nu}(\mathbf{k})=\frac{1}{N_L}\sum_{i,j} \exp[i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j)] \chi^{\mu\nu}_{ij}
Args
obsfile:str- Path to the obsfile.
momentum:Union[list,numpy.array]- Momentum points at which to compute the structure factor. Can be a one-dimensional list or array of three kx,ky,kz coordinates, or a two-dimensional list or array of multiple momentum points.
cutoff:Union[float,list,numpy.array,str], optional- Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all".
component:str, optional- Spin component of the structure factor to retrieve. Can be "XX", "XY", "XZ", "YX", …, "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all".
verbose:bool, optional- Defines whether the output should be verbose. Defaults to True.
Returns
Union[dict,numpy.ndarray]- If
verbose==False, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of momentum points specified. If the output is verbose, return a dict with keysdata(contains the nonverbose data),cutoff(contains the selected cutoff values), andmomentum(momentum points).
Expand source code
def getStructureFactor(obsfile, momentum, cutoff="all", component="all", verbose=True): r""" Calculate the spin structure factor from the spin correlations stored in an observable file. The structure factor is defined as the Fourier transform of the real-space correlations \( \chi^{\mu\nu}_{ij} \), normalized by the number of lattice sites, \( N_L \). See the SpinParser documentation for information on the real-space correlations. The expression for the structure factor is given by \[ \chi^{\mu\nu}(\mathbf{k})=\frac{1}{N_L}\sum_{i,j} \exp[i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j)] \chi^{\mu\nu}_{ij} \] Args: obsfile (str): Path to the obsfile. momentum (Union[list,numpy.array]): Momentum points at which to compute the structure factor. Can be a one-dimensional list or array of three kx,ky,kz coordinates, or a two-dimensional list or array of multiple momentum points. cutoff (Union[float,list,numpy.array,str], optional): Cutoff values at which to retrieve data. Can be a single cutoff value, a list of cutoff values, or "all". Defaults to "all". component (str, optional): Spin component of the structure factor to retrieve. Can be "XX", "XY", "XZ", "YX", ..., "ZZ", or "all". The latter is equivalent to obtaining the sum of "XX", "YY", and "ZZ". Defaults to "all". verbose (bool, optional): Defines whether the output should be verbose. Defaults to True. Returns: Union[dict,numpy.ndarray]: If `verbose==False`, return an array of shape (N,M) where N is the number of cutoff values selected and N is the number of momentum points specified. If the output is verbose, return a dict with keys `data` (contains the nonverbose data), `cutoff` (contains the selected cutoff values), and `momentum` (momentum points). """ #parse argument `momentum` if type(momentum) == list: momentum = np.array(momentum) if momentum.ndim == 1: momentum = np.reshape(momentum, (1,len(momentum))) if not (momentum.ndim == 2 and momentum.shape[1] == 3): raise Exception("Invalid argument type: momentum") #get correlation basis = getLatticeBasis(obsfile) cutoffList = getCorrelation(obsfile, cutoff=cutoff, site="all", reference=0, component=component, verbose=True)["cutoff"] data = np.zeros((len(cutoffList),len(momentum)), dtype=np.float32) for i in range(len(basis)): raw = getCorrelation(obsfile, cutoff=cutoff, site="all", reference=i, component=component, verbose=True) for i_c in range(len(raw["cutoff"])): for i_k in range(len(momentum)): for i_s in range(len(raw["site"])): data[i_c,i_k] += raw["data"][i_c,i_s] * np.cos(np.dot(momentum[i_k], raw["site"][i_s] - raw["reference"])) data /= len(basis) out = {"data":data, "cutoff":cutoffList, "momentum":momentum} #return data return out if verbose else out["data"]