matrix

Creates a numerical matrix with real (matrix) or complex (matrixC) coefficients given an Op or OpSum on a certain block.

Sources
matrix.hpp
matrix.cpp
matrix.jl

---

Definition

A matrix can be created in two ways:

1. Only the input block on which the operator is defined is given. The output block is calculated and eventually created automatically.

   C++Julia

   arma::mat matrix(Op const &op, Block const &block);
   arma::mat matrix(OpSum const &ops, Block const &block);
   arma::cx_mat matrixC(Op const &op, Block const &block);
   arma::cx_mat matrixC(OpSum const &ops, Block const &block);
   

   matrix(op::Op, block::Block)
   matrix(ops::OpSum, block::Block)
   

Comment: In Julia, depending on whether a real/complex matrix is generated also a real/complex matrix is returned. The C++ version has to return a fixed type. If a real matrix is desired, use the functions coo_matrix or coo_matrix_32. If a complex matrix is desired, use the functions coo_matrixC and coo_matrixC_32.

---

Parameters

Name	Description
ops	OpSum or Op defining the operator
block / block_in	input block on which the operator is defined
block_out	output block the operator maps the input block to

---

Usage Example

C++Julia

// Creates matrix H_{k=2} in Eq (18.23) of https://link.springer.com/content/pdf/10.1007/978-3-540-74686-7_18.pdf
int N = 4;
int nup = 3;
int ndn = 2;

// Define a Hubbard chain model
auto ops = OpSum();
for (int i=0; i< N; ++i){
  ops += "T" * Op("Hop", {i, (i+1) % N});
}
ops+= "U" * Op("HubbardU");
ops["T"] = 1.0;
ops["U"] = 5.0;

// Create the a permutation group
auto p1 = Permutation({0, 1, 2, 3});
auto p2 = Permutation({1, 2, 3, 0});
auto p3 = Permutation({2, 3, 0, 1});
auto p4 = Permutation({3, 0, 1, 2});
auto group = PermutationGroup({p1, p2, p3, p4});
auto irrep = Representation(group, arma::vec{1.0, -1.0, 1.0, -1.0});
auto block = Electron(N, nup, ndn, irrep);
auto H = matrix(ops, block);
H.print();

let
    # Creates matrix H_{k=2} in Eq (18.23) of https://link.springer.com/content/pdf/10.1007/978-3-540-74686-7_18.pdf
    N = 4
    nup = 3
    ndn = 2

    # Define a Hubbard chain model
    ops = OpSum()
    for i in 1:N
        ops += "T" * Op("Hop", [i, mod1(i+1, N)])
    end
    ops += "U" * Op("HubbardU")
    ops["T"] = 1.0;
    ops["U"] = 5.0;

    # Create the a permutation group
    p = Permutation([2, 3, 4, 1])
    group = PermutationGroup([p^0, p^1, p^2, p^3])
    irrep = Representation(group, [1.0, -1.0, 1.0, -1.0])
    block = Electron(N, nup, ndn, irrep)

    H = matrix(ops, block)
    display(H)
end