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Journal of the Physical Society of Japan

Commensurate and Incommensurate Transitions for Interacting Particles

Cosima Schuster, Rudolf A. Römer, Michael Schreiber

Published Jan 3, 2003• 1 citation
Publisher
DOI
10.1143/jpsjs.72sa.129

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We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-Andr\'e chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations --- in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach.
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.