Skip to content

expect

Computes the expectation value of a single-site operator on every site of a State, returning a vector whose \(i\)-th entry is \(\langle \psi | \mathcal{O}_i | \psi \rangle\). This is convenient for evaluating quantities such as the local magnetization \(\langle S^z_i \rangle\) or the local density \(\langle n_i \rangle\) in a single call.

Sources: expect.hpp ยท expect.cpp

Definition

expect(state::State, type::String)

arma::vec expect(State const &state, std::string type);
arma::cx_vec expectC(State const &state, std::string type);

The function expect returns a real result and raises an error if the result is complex; in that case use expectC in C++. In Julia, expect returns a real or complex vector as appropriate.

Parameters

Name Description
state the State \(\lvert\psi\rangle\) the expectation value is evaluated on (assumed normalized)
type the type of a single-site operator (e.g. "Sz", "N", "Ntot")

Returns

A vector of length nsites, whose \(i\)-th entry is \(\langle \psi | \mathcal{O}_i | \psi \rangle\) with \(\mathcal{O}_i\) the operator of the given type acting on site \(i\).

Info

The state is assumed to be normalized; the raw matrix elements are returned without dividing by \(\langle \psi | \psi \rangle\). The operator must keep the state within its block; an operator that changes a conserved quantum number is reported as a block mismatch.

Usage Example

let
    block = Spinhalf(8)
    ops = OpSum()
    for i in 1:8
    ops += "J" * Op("SdotS", [i, mod1(i + 1, 8)])
    end
    ops["J"] = 1.0
    e0, psi0 = eig0(ops, block)
    szs = expect(psi0, "Sz")
end

auto block = Spinhalf(8);
auto ops = OpSum();
for (int i = 0; i < 8; ++i) {
  ops += "J" * Op("SdotS", {i, (i + 1) % 8});
}
ops["J"] = 1.0;
auto [e0, psi0] = eig0(ops, block);
arma::vec sz = expect(psi0, "Sz");