Op

Object describing a single linear operator acting on a Hilbert space.

Sources
op.hpp
op.cpp
op.jl

---

Every operator is defined by up to three paramaters:

1. The type of the operator. This is a string argument which determines what kind of operator is represented. A detailed overview of the available types can be found at Operator types

2. The sites of the operator. This defines which physical sites (or orbitals) the operator acts upon. While most operator types require sites, there are also operator types (e.g. HubbardU) which do not need to define sites.

3. For special interactions, it can be necessary to additionally specify a numerical matrix, which can either be real or complex. An example is the operator type Matrix defining generic spin interactions.

---

Constructors

C++Julia

Op(std::string type);
Op(std::string type, int64_t site);
Op(std::string type, std::vector<int64_t> const &sites);
Op(std::string type, int64_t site, arma::mat const &matrix);
Op(std::string type, std::vector<int64_t> const &sites, arma::mat const &matrix);
Op(std::string type, int64_t site, arma::cx_mat const &matrix);
Op(std::string type, std::vector<int64_t> const &sites, arma::cx_mat const &matrix);

Op(type::String)
Op(type::String, site::Int64)
Op(type::String, sites::Vector{Int64})
Op(type::String, site::Int64, matrix::Matrix{Float64})
Op(type::String, sites::Vector{Int64}, matrix::Matrix{Float64})
Op(type::String, site::Int64, matrix::Matrix{ComplexF64})
Op(type::String, sites::Vector{Int64}, matrix::Matrix{ComplexF64})

Parameter	Description
type	a string which denotes what kind of operator is represented
sites	defines on which site(s) of the lattice the operator acts on.	optional
matrix	defines a matrix which may be needed to describe an operator.	optional

1-indexing in Julia / 0-indexing in C++

To enumerate the sites of an Op, we start counting at 1 in Julia and 0 in C++.

---

Methods

isreal

Returns whether an Op is a real operator.

C++Julia

bool isreal(Op const &op);

isreal(op::Op)::Bool

---

isapprox

Returns whether two Ops are approximately equal.

C++Julia

bool isapprox(Op const &op1, OpSum const &op2, double rtol = 1e-12,
              double atol = 1e-12);

isapprox(op1::Op, op2::Op, rtol::Float64=1e-12, atol::Float64=1e-12)::Bool

---

to_string (operator<<)

Converts the Op to a readable string representation.

C++Julia

std::string to_string(Op const &op);
std::ostream &operator<<(std::ostream &out, Op const &op);

to_string(op::Op)::String

---

Usage Example

C++Julia

auto op = "T" * Op("Hop", {0, 1});
XDIAG_SHOW(op);

op = 1.23 * Op("Hop", {0, 1});
XDIAG_SHOW(op);

arma::cx_mat m(arma::mat("0 0; 0 0"), arma::mat("0 -1; 1 0"));
op = Op("Matrix", 0, m);
XDIAG_SHOW(op);
XDIAG_SHOW(isreal(op));

op = "T" * Op("Hop", [1, 2])
@show op

op = 1.23 * Op("Hop",  [1, 2])
@show op

op = Op("Matrix", 1, [0 -1.0im; 1.0im 0])
@show op
@show isreal(op)