Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1405.2902 · Journal of the Physical Society of Japan

A Density-Matrix Renormalization Group Study of a One-Dimensional Incommensurate Quantum Frenkel–Kontorova Model

Yongjun Ma, Jiaxiang Wang, Xinye Xu, Qi Wei, Wenjun Zhu, Sabre Kais

Published Aug 22, 2014• 2 citations
arXivHTMLPDF

Abstract

In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova model is investigate by a density-matrix renormalization group algorithm. Special attention is given to the entanglement and the ground state energy. The energy gap between the ground state and the first excited is also calculated. From all the numerical results, we have observed an obvious property changes from the pinned state to the sliding one as the quantum fluctuation is increased. But no expected quantum critical point can be justified by the present data.

DOI
10.7566/jpsj.83.094605

Related papers

Quantum Phase Transition in One-Dimensional Commensurate Frenkel–Kontorova Model

Yongjun Ma, Jiaxiang Wang, Xinye Xu +2 more

In this paper, we have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of the entanglement, the coordinate correlation, the ground state energy and the energy gap between the ground state and the first excited one. It is demonstrated that a quantum phase transition (QPT) between the pinned and the sliding phases takes place as the quantum fluctuation, measured by an effective Planck constant $\tilde\hbar$, increases to a threshold value $\tilde \hbar_c$.

arXiv:1405.2901•Journal of the Physical Society of Japan•Dec 1, 2014•3 citations

Density-matrix renormalization group study of the incommensurate quantum Frenkel-Kontorova model

B. Hu, J. X. Wang

By using the density-matrix renormalization group technique, the incommensurate quantum Frenkel-Kontorova model is investigated numerically. It is found that when the quantum fluctuation is strong enough, the $g$ function featured by a sawtooth map in the depinned state will show a different kind of behavior, similar to a standard map, but with reduced magnitude. The related position correlations are studied in detail, which leads to a potentially interesting application to the recently well-explored phase transitions in cold atoms loaded in optical lattices.

arXiv:cond-mat/0604077•Physical Review B•May 23, 2006•7 citations

Application of the t-Adaptive Density Matrix Renormalization Group Method to the Quantum Frenkel-Kontorova Model

Jiaxiang Wang, Bambi Hu, XiaoqunWang XiaoqunWang

In this paper, the t-adaptive density matrix renormalization group method has been applied to study the dynamics of the one-dimensional quantum Frenkel-Kontorova model. It is found that as the quantum fluctuations increase, the local excitations will become unstable. The unstableness will lead to the dominance of the phonon excitations as the elementary excitations of the system in the deep quantum regime.

Progress of Theoretical Physics Supplement•Jan 1, 2007•2 citations

Ground-state wave function of the quantum Frenkel-Kontorova model

Bingcheng Hu, Baowen Li

The wave function of an incommensurate ground state for a one-dimensional discrete sine-Gordon model—the Frenkel-Kontorova (FK) model—at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wave function crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.

arXiv:cond-mat/9904287•Europhysics Letters (EPL)•Jun 1, 1999•13 citations

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

O. V. Zhirov, Giulio Casati, Dima L. Shepelyansky

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime where 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 Planck smaller than the critical value Planck(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 that have an exponentially small excitation energy. At Planck = Planck(c) the quantum phase transition takes place and for Planck > Planck(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 appearance of sliding modes at Planck > Planck(c).

arXiv:cond-mat/0210379•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•May 19, 2003•17 citations

Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

Juan José Mendoza-Arenas, R. Franco, Jereson Silva-Valencia

We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.

Physical Review B•Jan 8, 2010•11 citations
In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova model is investigate by a density-matrix renormalization group algorithm. Special attention is given to the entanglement and the ground state energy. The energy gap between the ground state and the first excited is also calculated. From all the numerical results, we have observed an obvious property changes from the pinned state to the sliding one as the quantum fluctuation is increased. But no expected quantum critical point can be justified by the present data.
In this paper, we have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of the entanglement, the coordinate correlation, the ground state energy and the energy gap between the ground state and the first excited one. It is demonstrated that a quantum phase transition (QPT) between the pinned and the sliding phases takes place as the quantum fluctuation, measured by an effective Planck constant ℏ~\tilde\hbarℏ~, increases to a threshold value ℏ~c\tilde \hbar_cℏ~c​.
By using the density-matrix renormalization group technique, the incommensurate quantum Frenkel-Kontorova model is investigated numerically. It is found that when the quantum fluctuation is strong enough, the ggg function featured by a sawtooth map in the depinned state will show a different kind of behavior, similar to a standard map, but with reduced magnitude. The related position correlations are studied in detail, which leads to a potentially interesting application to the recently well-explored phase transitions in cold atoms loaded in optical lattices.
The wave function of an incommensurate ground state for a one-dimensional discrete sine-Gordon model—the Frenkel-Kontorova (FK) model—at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wave function crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.
We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime where 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 Planck smaller than the critical value Planck(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 that have an exponentially small excitation energy. At Planck = Planck(c) the quantum phase transition takes place and for Planck > Planck(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 appearance of sliding modes at Planck > Planck(c).
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.