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

Physical Review B

Nonadiabatical approach to the Dzyaloshinsky-Moriya interaction in the XY spin chain coupled with quantum phonons

Qin Wang, Hang Zheng

Published Nov 4, 2004• 1 citation
Publisher

Abstract

Using the model of the DM interaction in $XY$ antiferromagnetic spin chain with spin-phonon coupling, the nonadiabatic effects on the DM interaction have been studied by developing a nonadiabatic analytical approach. The results show that in the nonadiabatic case, to a certain finite phonon frequency, there exists a finite critical value of spin-phonon coupling. As the spin-phonon coupling decreases to the critical value, the system becomes gapless and the spin dimerization is destroyed. The DM interaction leads the system to have a finite critical value of spin-phonon coupling even in the adiabatic limit. The increase in staggered DM interaction will decrease the critical value of spin-phonon coupling, but increase that of phonon frequency, therefore, favors the dimerization. The nonadiabaticity plays an important role in suppressing the enhancement effects of the DM interaction to the dimerization. The dimerized ground state when DM interaction is present can be destroyed by the quantum lattice fluctuations. The threshold value of $\ensuremath{\beta}$ changing the effect of the DM interaction on the dimerization from suppression to promotion is not simply a constant but a crossover. For appropriate fixed values of spin-phonon coupling, phonon frequency and $\ensuremath{\beta}$, as $D$ increases, the system undergoes a reentry of phase between spin-dimer state and gapless state.

DOI
10.1103/physrevb.70.184405

Related papers

Phase diagram and correlation function of a spin-Peierls system in the ground state: Effects of the quantum lattice fluctuations

Qin Wang, Hang Zheng, Hong Chen

Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.

Physical review. B, Condensed matter•Mar 29, 2002•6 citations

Effect of quantum lattice fluctuations on the dimerized ground state of the Takayama-Lin-Liu-Maki model

Hongxing Zheng, D. L. Lin, Thomas F. George

The effect of quantum lattice fluctuations on the dimerized ground state is studied in the half-filled-band Takayama-Lin-Liu-Maki model. The nonadiabatic effect due to finite phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$\ensuremath{\gtrsim}0 is treated through an energy-dependent electron-phonon scattering function \ensuremath{\delta}(${\mathit{k}}^{\ensuremath{'}}$,k) introduced by means of a unitary transformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state and results in four-fermion interaction. By decoupling of the electronic correlations we show that our approach gives a good description of the continuous variation of the dimerization as functions of the dimensionless coupling constant ${\mathit{g}}^{2}$ and the phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ when the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t (t is the electron hopping integral) is not large. Our results show that, at least in the weak-coupling limit, quantum lattice fluctuations change the functional dependence of the dimerization parameter ${\mathit{m}}_{\mathit{p}}$ on the coupling constant even if the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is small (but finite). In the spin-1/2 case our result is the same as that predicted by Fradkin and Hirsch. But in the spinless case we still predict a long-range dimerization order even if the coupling is weak and ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is finite. In the large ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ (antiadiabatic) limit we show that our effective Hamiltonian becomes an n-component Gross-Neveu model and the ratio ${\mathit{m}}_{\mathit{p}}$(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=\ensuremath{\infty})/${\mathit{m}}_{\mathit{p}}$(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=0) is equal to 1/cosh(\ensuremath{\pi}/2${\mathit{ng}}^{2}$) (n=1: spinless; n=2: spin-1/2). By using the same input parameters as those of some previous authors we get a 7.2% reduction of the dimerization parameter ${\mathit{m}}_{\mathit{p}}$ compared with the adiabatic value. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 1, 1996•1 citation

The spin-Peierls instability in a spin- XY chain in the non-adiabatic limit

Shreekantha Sil

The spin-Peierls instability in a spin- XY chain coupled to dispersionless phonons of frequency has been studied in the non-adiabatic limit. We have chosen the Lang-Firsov variational wavefunction for the phonon subsystem to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then solved in the framework of the mean-field approximation and bond operator technique. We observed two types of phase transitions, one is from the spin liquid phase to the dimerized phase and the other is from the dimerized phase to the antiferromagnetic phase as we vary the spin-phonon coupling from a very low value. The variation of lattice distortion, dimerized order parameter and energy gap with spin-phonon coupling parameter have also been investigated here.

arXiv:cond-mat/9803378•Journal of Physics Condensed Matter•Oct 5, 1998•4 citations

The Dzyaloshinskii-Moriya interaction in spin-Peierls systems

Zhiguo Yang, Zhiguo Wang, Hong Chen

The influence of Dzyaloshinskii-Moriya (DM) interaction on the spin-Peierls systems is studied by use of theoretical analysis and the Lanczos numerical method. The ground sate of the spin-Peierls system is still a dimerized phase when DM interaction is present. The results show that the uniform DM interaction is always against dimerization but the staggered DM interaction may act in favour of or against dimerization. There exists a critical point where the staggered DM interaction has no influence on dimerization.

Journal of Physics Condensed Matter•Feb 15, 2002•10 citations

Adiabatic-antiadiabatic crossover in a spin-Peierls chain

R. Citro, E. Orignac, Thierry Giamarchi

We consider an $XXZ$ spin-$1∕2$ chain coupled to optical phonons with nonzero frequency ${\ensuremath{\omega}}_{0}$. In the adiabatic limit (small ${\ensuremath{\omega}}_{0}$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ${\ensuremath{\omega}}_{0}$), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\Delta}}_{s}$, where ${\ensuremath{\Delta}}_{s}$ is the gap in the static limit ${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}0$, the system is in the adiabatic regime, and the gap remains of order ${\ensuremath{\Delta}}_{s}$. For ${\ensuremath{\omega}}_{0}>{\ensuremath{\Delta}}_{s}$, the system enters the antiadiabatic regime, and the gap decreases rapidly as ${\ensuremath{\omega}}_{0}$ increases. Finally, for ${\ensuremath{\omega}}_{0}>{\ensuremath{\omega}}_{\mathit{BKT}}$, where ${\ensuremath{\omega}}_{\mathit{BKT}}$ is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.

arXiv:cond-mat/0411256•Physical Review B•Jul 15, 2005•38 citations

Quantum critical phenomena in the XY spin chain with the Dzyaloshinski-Moriya interaction (Retracted article. See vol 80, artn 019903, 2009)

YC Li, Li Ss

We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.

•Jan 1, 2009•0 citations
Using the model of the DM interaction in XYXYXY antiferromagnetic spin chain with spin-phonon coupling, the nonadiabatic effects on the DM interaction have been studied by developing a nonadiabatic analytical approach. The results show that in the nonadiabatic case, to a certain finite phonon frequency, there exists a finite critical value of spin-phonon coupling. As the spin-phonon coupling decreases to the critical value, the system becomes gapless and the spin dimerization is destroyed. The DM interaction leads the system to have a finite critical value of spin-phonon coupling even in the adiabatic limit. The increase in staggered DM interaction will decrease the critical value of spin-phonon coupling, but increase that of phonon frequency, therefore, favors the dimerization. The nonadiabaticity plays an important role in suppressing the enhancement effects of the DM interaction to the dimerization. The dimerized ground state when DM interaction is present can be destroyed by the quantum lattice fluctuations. The threshold value of \ensuremathβ\ensuremath{\beta}\ensuremathβ changing the effect of the DM interaction on the dimerization from suppression to promotion is not simply a constant but a crossover. For appropriate fixed values of spin-phonon coupling, phonon frequency and \ensuremathβ\ensuremath{\beta}\ensuremathβ, as DDD increases, the system undergoes a reentry of phase between spin-dimer state and gapless state.
Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.
The effect of quantum lattice fluctuations on the dimerized ground state is studied in the half-filled-band Takayama-Lin-Liu-Maki model. The nonadiabatic effect due to finite phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$\ensuremath{\gtrsim}0 is treated through an energy-dependent electron-phonon scattering function \ensuremath{\delta}(${\mathit{k}}^{\ensuremath{'}}$,k) introduced by means of a unitary transformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state and results in four-fermion interaction. By decoupling of the electronic correlations we show that our approach gives a good description of the continuous variation of the dimerization as functions of the dimensionless coupling constant g2{\mathit{g}}^{2}g2 and the phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ when the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t (t is the electron hopping integral) is not large. Our results show that, at least in the weak-coupling limit, quantum lattice fluctuations change the functional dependence of the dimerization parameter mp{\mathit{m}}_{\mathit{p}}mp​ on the coupling constant even if the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is small (but finite). In the spin-1/2 case our result is the same as that predicted by Fradkin and Hirsch. But in the spinless case we still predict a long-range dimerization order even if the coupling is weak and ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is finite. In the large ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ (antiadiabatic) limit we show that our effective Hamiltonian becomes an n-component Gross-Neveu model and the ratio mp{\mathit{m}}_{\mathit{p}}mp​(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=\ensuremath{\infty})/mp{\mathit{m}}_{\mathit{p}}mp​(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=0) is equal to 1/cosh(\ensuremath{\pi}/2ng2{\mathit{ng}}^{2}ng2) (n=1: spinless; n=2: spin-1/2). By using the same input parameters as those of some previous authors we get a 7.2% reduction of the dimerization parameter mp{\mathit{m}}_{\mathit{p}}mp​ compared with the adiabatic value. \textcopyright{} 1996 The American Physical Society.
The spin-Peierls instability in a spin- XY chain coupled to dispersionless phonons of frequency has been studied in the non-adiabatic limit. We have chosen the Lang-Firsov variational wavefunction for the phonon subsystem to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then solved in the framework of the mean-field approximation and bond operator technique. We observed two types of phase transitions, one is from the spin liquid phase to the dimerized phase and the other is from the dimerized phase to the antiferromagnetic phase as we vary the spin-phonon coupling from a very low value. The variation of lattice distortion, dimerized order parameter and energy gap with spin-phonon coupling parameter have also been investigated here.
The influence of Dzyaloshinskii-Moriya (DM) interaction on the spin-Peierls systems is studied by use of theoretical analysis and the Lanczos numerical method. The ground sate of the spin-Peierls system is still a dimerized phase when DM interaction is present. The results show that the uniform DM interaction is always against dimerization but the staggered DM interaction may act in favour of or against dimerization. There exists a critical point where the staggered DM interaction has no influence on dimerization.
We consider an XXZXXZXXZ spin-1∕21∕21∕2 chain coupled to optical phonons with nonzero frequency ${\ensuremath{\omega}}_{0}$. In the adiabatic limit (small ${\ensuremath{\omega}}_{0}$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ${\ensuremath{\omega}}_{0}$), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\Delta}}_{s}$, where ${\ensuremath{\Delta}}_{s}$ is the gap in the static limit ${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}0$, the system is in the adiabatic regime, and the gap remains of order ${\ensuremath{\Delta}}_{s}$. For ${\ensuremath{\omega}}_{0}>{\ensuremath{\Delta}}_{s}$, the system enters the antiadiabatic regime, and the gap decreases rapidly as ${\ensuremath{\omega}}_{0}$ increases. Finally, for ${\ensuremath{\omega}}_{0}>{\ensuremath{\omega}}_{\mathit{BKT}}$, where ${\ensuremath{\omega}}_{\mathit{BKT}}$ is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.
We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.