Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

Abstract

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations we show that for the effective Planck constant $\hslash$ smaller than the critical value ${\hslash }_c$ the quantum chain is in the pinned instanton glass phase. In this phase the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons which have an exponentially small excitation energy. At $\hslash ={\hslash }_c$ the quantum phase transition takes place and for $\hslash >{\hslash }_c$ the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearence of sliding modes at $\hslash >{\hslash }_c$.

revtex 16 pages, 18 figures

References in corpus (9)

• Instantons in QCD
• Continuous Quantum Phase Transitions
• Dynamical transitions in correlated driven diffusion in a periodic potential
• Onset of sliding friction in incommensurate systems
• The quantum Frenkel-Kontorova model: a squeezed state approach
• Quantum Frenkel-Kontorova Model
• Ground state wavefunction of the quantum Frenkel-Kontorova model
• Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain
• Mode-locking of incommensurate phase by quantum zero point energy in the Frenkel-Kontorova model

Cited by in corpus (14)

• Trapped ions in optical lattices for probing oscillator chain models
• Frenkel-Kontorova model with cold trapped ions
• Nano-friction in cavity quantum electrodynamics
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Quantum Effects in the Aubry Transition
• Quantum nanofriction in trapped ion chains with a topological defect
• Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model
• Wigner crystal in snaked nanochannels
• Quantum compacton vacuum
• Quantum phase transition in one-dimensional commensurate Frenkel-Kontorova model
• Soft quantum vibrations of PT-symmetric nonlinear ion chain
• A density-matrix renormalization group Study of one-dimensional incommensurate quantum Frenkel-Kontorova model
• Renormalization and Quantum Scaling of Frenkel-Kontorova Models
• Wigner crystal in snaked nanochannels: outlook