Documentation for ITensorsOpenSystems.GlobalFunctionApproximation

augustbanuls(funcs,A,U0,maxiter;kwargs...)

augustbanuls(
func::Function,
A::ITensors.MPO,
U0::ITensors.MPO,
maxiter::Int;
kwargs...,)

Evaluates functions of the form Tr[f(A)], where A is a Hermian operator given as an MPO and f is an arbirary function, using the algorithm in August,Banuls (2018).

Accepts either a single function or a list of functions [f,g,h...] to evaluate Tr[f(A)],Tr[g(A)],Tr[h(A)]... simultaniously, as this is substantially more efficent that running the algorithm separately for each function.

Arguments

• funcs: The function or list of functions to be evaluated on the target matrix
• A: The argument Hermitian matrix on which the functions are to act
• U0: A unitary matrix, given as an MPO with the same set of indices as m which acts as an inital value of the iteration
• maxiter: The maximum number of loops of the algorithm, after which it will terminate and return the result, even if the desired convergence has not been achieved

Key word arguments

• tol: The maximum desired error for the algorithm to terminate
• cuttoff, maxdim, mindim: Determine the truncation conditions for the MPO operations in the usual way, the same as for built in ITensors functions.

Returns

• The trace or traces of the functions either as a single number or vector of traces