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Effective phonon treatment of asymmetric interparticle interaction potentials

We propose an effective phonon treatment in one dimensional momentum-conserved lattice system with asymmetric interparticle interaction potentials. Our strategy is to divide the potential into two segments by the zero-potential point, and then approximate them by piecewise harmonic potentials with effective force constants $\tilde{k}_L$ and $\tilde{k}_R$ respectively. The effective phonons can then be well described by $ω_c=\sqrt{2(\tilde{k}_L+\tilde{k}_R)}% |sin(\frac{1}{2}aq)|$. The numerical verifications show that this treatment works very well.