Simple variational approach to the quantum Frenkel-Kontorova model - art. no. 016203

We present a simple and complete variational approach to the one-dimensiona l quantum Frenkel-Kontorova model. Dirac's time-dependent variational princ iple is adopted together with a Hartree-type many-body trial wave function for the atoms. The single-particle state is assumed to have the Jackiw-Kerm an form. We obtain an effective classical Hamiltonian for the system, which is simple enough for a complete numerical solution for the static ground s tate of the model. Numerical results show that our simple approach captures the essence of the quantum effects first observed in quantum Monte Carlo s tudies.