Classical dynamics of S=1/2 spin ladders using SU(4) coherent states

The Landau-Lifshitz equations of motion can be derived by taking the classical limit of a spin system based on SU(2) coherent states. Generalizing this procedure from SU(2) to SU(N) gives a classical dynamics of SU(N) coherent states, where N >2 is the dimension of the local Hilbert space. Among other applications, this generalization can be used to model coupled units with strong intra-unit entanglement. For example, the quantum mechanical states of a dimer of two antiferromagnetically coupled S=1/2 spins are SU(4) coherent states. These coherent states include for instance the singlet, which does not have a classical counterpart in the traditional Landau-Lifshitz dynamics. In particular, we can describe a spin ladder of weakly coupled dimers as a chain of SU(4) spins. By using the corresponding classical limit based on SU(4) coherent states, we compute the zero and finite temperature dynamics of the spin ladder and compare against density matrix renormalization group (DMRG) calculations. In the regime where the inter-dimer exchange is not too large, the SU(4) results agree well with DMRG, while requiring only a small fraction of the computational cost.