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:cond-mat/9902230 · Physical Review Letters

Spin-Peierls Transition in the Heisenberg Chain with Finite-Frequency Phonons

Anders W. Sandvik, David K Campbell

Published Jul 5, 1999• 59 citations
arXivHTMLPDF

Abstract

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}256$ spins show unambiguously that the transition occurs only when the spin-phonon coupling $\ensuremath{\alpha}$ exceeds a critical value ${\ensuremath{\alpha}}_{c}$. Using sum rules, we show that the phonon spectral function has divergent (for $N\ensuremath{\rightarrow}\ensuremath{\infty}$) weight extending to zero frequency for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$. The phonon correlations decay with distance $r$ as $1/r$. This behavior is characteristic for all $0<\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ and the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$ phonon does not soften (to zero frequency) at $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\alpha}}_{c}$.

DOI
10.1103/physrevlett.83.195

Related papers

Néel to spin-Peierls transition in a quasi-one-dimensional Heisenberg model coupled to bond phonons

Jason C. Pillay, Keola Wierschem, Pinaki Sengupta

The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-$\frac{1}{2}$ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature ${T}_{c}$ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to ${T}_{c}$, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.

arXiv:1310.0880•Physical Review B•Aug 22, 2013•2 citations

Neel to spin-Peierls transition in the ground state of a quasi-1D Heisenberg model coupled to bond phonons

Pinaki Sengupta

The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model, where adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon coupling. The phase diagram in the above parameter space is mapped out. No evidence is found for a region of co-existing long range magnetic order and dimerization. The vanishing of the Neel order occurs simultaneously with the setting in of the dimerization.

arXiv:cond-mat/0307746•Jul 30, 2003•0 citations

Lattice dynamics of the Heisenberg chain coupled to finite frequency bond phonons

Franz Michel, Hans-Gerd Evertz

The phonon dynamics in a one dimensional Heisenberg spin chain coupled to finite-frequency bond phonons is studied. We present the first detailed phonon spectra for these systems using Quantum Monte Carlo. The quantum phase transition is dominated by a central peak, yet the renormalisation of the main phonon branch depends strongly on the bare phonon frequency omega_0. The main branch remains largely unaffected at omega_0 \gsim J, but it softens completely when omega_0 is low enough. This is an unusual scenario for a structural phase transition and was observable only on sufficiently large systems. Approaching the dimerized phase from finite temperature, the lattice dynamics mirrors the behavior of a three dimensional system. For the efficient measurement of Greens functions, we introduce a mapping from the stochastic series expansion to continuous imaginary time.

arXiv:0705.0799•May 7, 2007•3 citations

Thermodynamics of Heisenberg chains coupled to phonons

Rainer Walter Kühne

The one-dimensional spin-1/2 Heisenberg model with nearest-neighbour interaction coupled to Einstein phonons is of interest for the understanding of materials which show the spin-Peierls phase transition. I examined this model by performing a finite-temperature quantum Monte Carlo simulation by using the very efficient loop algorithm. I studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-spin correlation function of this model for various spin-phonon couplings and phonon frequencies. In particular I gave evidence for a global effective spin-spin coupling and for the transition from a gapless to the massive phase by studying the finite-size behavior of the magnetic susceptibility.

•Jul 19, 2001•0 citations

Phase diagram of the spin-Peierls chain with local coupling: Density-matrix renormalization-group calculations and unitary transformations

Alexander Weiße, Georg Hager, A. R. Bishop +1 more

We explore the ground-state phase diagram of a Heisenberg spin chain coupled locally to optical phonons (bond coupling), using large-scale density-matrix renormalization-group calculations and extending a unitary transformation approach which removes the spin-phonon coupling in leading order. For the quantum phase transition from the spin liquid to the dimerized phase, we find deviations from previous quantum Monte Carlo and flow equation results.

arXiv:cond-mat/0607209•Physical Review B•Dec 27, 2006•16 citations

Critical Behavior of Heisenberg Chains Coupled to Phonons

Rainer Walter Kühne

We present a quantum Monte Carlo study for the isotropic antiferromagnetic Heisenberg chain coupled to Einstein phonons. By investigating the behavior of the correlation length we find the critical exponent to depend on both the phonon frequency and the spin-phonon coupling constant. Hence, these systems change the universality class continuously with the spin-phonon coupling.

•Mar 11, 2019•0 citations
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}256N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling \ensuremathα\ensuremath{\alpha}\ensuremathα exceeds a critical value \ensuremathαc{\ensuremath{\alpha}}_{c}\ensuremathαc​. Using sum rules, we show that the phonon spectral function has divergent (for N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞) weight extending to zero frequency for \ensuremathα<\ensuremathαc\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}\ensuremathα<\ensuremathαc​. The phonon correlations decay with distance rrr as 1/r1/r1/r. This behavior is characteristic for all 0<\ensuremathα<\ensuremathαc0<\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}0<\ensuremathα<\ensuremathαc​ and the q=\ensuremathπq\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}q=\ensuremathπ phonon does not soften (to zero frequency) at \ensuremathα=\ensuremathαc\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\alpha}}_{c}\ensuremathα=\ensuremathαc​.
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model, where adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon coupling. The phase diagram in the above parameter space is mapped out. No evidence is found for a region of co-existing long range magnetic order and dimerization. The vanishing of the Neel order occurs simultaneously with the setting in of the dimerization.
The phonon dynamics in a one dimensional Heisenberg spin chain coupled to finite-frequency bond phonons is studied. We present the first detailed phonon spectra for these systems using Quantum Monte Carlo. The quantum phase transition is dominated by a central peak, yet the renormalisation of the main phonon branch depends strongly on the bare phonon frequency omega_0. The main branch remains largely unaffected at omega_0 \gsim J, but it softens completely when omega_0 is low enough. This is an unusual scenario for a structural phase transition and was observable only on sufficiently large systems. Approaching the dimerized phase from finite temperature, the lattice dynamics mirrors the behavior of a three dimensional system. For the efficient measurement of Greens functions, we introduce a mapping from the stochastic series expansion to continuous imaginary time.
The one-dimensional spin-1/2 Heisenberg model with nearest-neighbour interaction coupled to Einstein phonons is of interest for the understanding of materials which show the spin-Peierls phase transition. I examined this model by performing a finite-temperature quantum Monte Carlo simulation by using the very efficient loop algorithm. I studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-spin correlation function of this model for various spin-phonon couplings and phonon frequencies. In particular I gave evidence for a global effective spin-spin coupling and for the transition from a gapless to the massive phase by studying the finite-size behavior of the magnetic susceptibility.