Commensurate-incommensurate transition in frustrated Wigner crystals
- URL: http://arxiv.org/abs/2311.14396v1
- Date: Fri, 24 Nov 2023 10:29:55 GMT
- Title: Commensurate-incommensurate transition in frustrated Wigner crystals
- Authors: Rapha\"el Menu, Jorge Yago Malo, Vladan Vuleti\'c, Maria Luisa
Chiofalo, Giovanna Morigi
- Abstract summary: This work is a paradigmatic realization of the Frenkel-Kontorova model with Coulomb interactions.
The mismatch between the periodicities of potential and chain, giving rise to frustration, is a chemical potential whose amplitude is majorly determined by the Coulomb self-energy.
For finite systems, however, the ground state has a fractal structure that could be measured in experiments with laser-cooled ions in traps.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: Geometric frustration in systems with long-range interactions is a largely
unexplored phenomenon. In this work we analyse the ground state emerging from
the competition between a periodic potential and a Wigner crystal in one
dimension, consisting of a selforganized chain of particles with the same
charge. This system is a paradigmatic realization of the Frenkel-Kontorova
model with Coulomb interactions. We derive the action of a Coulomb soliton in
the continuum limit and demonstrate the mapping to a massive (1+1) Thirring
model with long-range interactions. Here, the solitons are charged fermionic
excitations over an effective Dirac sea. The mismatch between the periodicities
of potential and chain, giving rise to frustration, is a chemical potential
whose amplitude is majorly determined by the Coulomb self-energy. The
mean-field limit is a long-range antiferromagnetic spin chain with uniform
magnetic field and predicts that the commensurate, periodic structures form a
complete devil's staircase as a function of the charge density. Each step of
the staircase correspond to the interval of stability of a stable commensurate
phase and scales with the number $N$ of charges as $1/\ln N$. This implies that
there is no commensurate-incommensurate phase transition in the thermodynamic
limit. For finite systems, however, the ground state has a fractal structure
that could be measured in experiments with laser-cooled ions in traps.
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