= Fourier vertex of a Schwinger boson chain
{title2=$H=-\frac JL\sum_{p,q,r,t}\delta^{(L)}_{p+q,r+t}\cos(q-t)A_p^\dagger B_q^\dagger B_rA_t$}
With the <Schwinger boson representation> and $a_n=L^{-1/2}\sum_qe^{-iqn}A_q$, the <Hamiltonian operator> of a periodic <quantum XY chain> takes the displayed form. The four <inverse discrete Fourier transforms> and site sum give $1/L$ and lattice <momentum conservation>. The forward and reverse nearest-neighbour exchange phases are $e^{i(q-t)}$ and $e^{-i(q-t)}$, giving the <cosine>. All <momenta> are defined modulo $2\pi$; neighbouring sites must be distinct for the stated <normal ordering>.
Back to article page
