The asymmetric three-state clock model is studied in the context of a one-dimensional quantum Hamiltonian. Series expansions are used to investigate the commensurate-incommensurate transition and the incommensurate-liquid Kosterlitz-Thouless transition. Evidence is presented for a Lifshitz point at which the critical indices $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ are Potts-type, while the mass-gap index appears to take its Ising value, $\ensuremath{\nu}=1$.The asymmetric three-state clock model is studied in the context of a one-dimensional quantum Hamiltonian. Series expansions are used to investigate the commensurate-incommensurate transition and the incommensurate-liquid Kosterlitz-Thouless transition. Evidence is presented for a Lifshitz point at which the critical indices $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ are Potts-type, while the mass-gap index appears to take its Ising value, $\ensuremath{\nu}=1$.

Physical review. B, Condensed matterFeb 1, 198355 citations

Commensurate and incommensurate ground states in a one-dimensional model

Béla Joós, B. Bergersen, Robert J Gooding +1 more

We present a renormalization argument for the discrete linear chain with a harmonic interparticle interaction and a sinusoidal substrate potential. We find that there exists a critical value of the substrate potential above which the incommensurate phase lying in between two successive registered phases is a complete devil's staircase of commensurate states. For weaker substrate potentials, the devil's staircase is partially incomplete. Near the commensurate-incommensurate transition it consists only of commensurate states, while at higher soliton densities the commensurate states are separated by truly incommensurate states. These results are in agreement with the findings of previous authors using different methods.We present a renormalization argument for the discrete linear chain with a harmonic interparticle interaction and a sinusoidal substrate potential. We find that there exists a critical value of the substrate potential above which the incommensurate phase lying in between two successive registered phases is a complete devil's staircase of commensurate states. For weaker substrate potentials, the devil's staircase is partially incomplete. Near the commensurate-incommensurate transition it consists only of commensurate states, while at higher soliton densities the commensurate states are separated by truly incommensurate states. These results are in agreement with the findings of previous authors using different methods.

Physical review. B, Condensed matterJan 1, 198312 citations

Commensurate and incommensurate correlations in Haldane-gap antiferromagnets

Gábor Fáth, András Sütö

We analyze the onset of incommensurabilities around the VBS point of the $S=1$ bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point ${\ensuremath{\theta}}_{\mathrm{VBS}}.$ Moreover, the theory predicts another special point ${\ensuremath{\theta}}_{\mathrm{disp}},$ distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.We analyze the onset of incommensurabilities around the VBS point of the $S=1$ bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point ${\ensuremath{\theta}}_{\mathrm{VBS}}.$ Moreover, the theory predicts another special point ${\ensuremath{\theta}}_{\mathrm{disp}},$ distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.

arXiv:cond-mat/0005211Physical review. B, Condensed matterAug 1, 200019 citations

We analyze the onset of incommensurabilities around the VBS point of the

S=1

bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point ${\ensuremath{\theta}}_{\mathrm{VBS}}.$ Moreover, the theory predicts another special point ${\ensuremath{\theta}}_{\mathrm{disp}},$ distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.