Seminarium Fizyki Materii Skondensowanej

The square-lattice S=1/2 Heisenberg antiferromagnet has long-range Neel order and gapless excitations, conventionally explained as Goldstone modes of spontaneously broken SU(2) symmetry. Yet numerical calculations recover the gapless spectrum in the thermodynamic limit without invoking symmetry breaking. To identify the underlying mechanism, we use an antiferromagnetic Jordan-Wigner fermion representation of the model, together with an equivalent hard-core boson (magnon) description, and introduce parameters that separately tune the magnon-magnon interactions and the Jordan-Wigner phases. We show that magnon-magnon interactions are crucial: they generate an entangled ground state and a divergent static spin structure factor, giving rise to gapless excitations without spontaneous symmetry breaking.