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

Acta Physica Sinica

THEORETICAL STUDY OF LOW-ENERGY ELEMENTARY EXCITATIONS IN SPIN-PEIERLS SYSTEM

Xu Jing, Chen Hong, Yumei Zhang, FENG WEI-GUO, 同济大学波耳固体物理研究所，上海 200092

Published Jan 1, 2000• 2 citations
Publisher

Abstract

By using bosonization technique and quantum self-consistent theory, we study the low-energy excitations of a spin-Peierls system. The ground state, one-particle excited state, two-particle bound state are calculated, and it is shown, as the frustration increases, the energy of the ground state decreases while the energy gap of the one- and two-particle states increases. By analysing the asymototic behavior of the longitudinal spin correlation function, we obtain that the two-particle bound state has similar spin structures as those of the singlet ground state. Thus, we regard the bound state as a singlet state, which exists between the ground state and the two-particle continuous excited state. Our results are qualitatively in agreement with the experimental phenomena observed by Ain et al. It is shown that the existence of bound state is one of the spin-Peierls system's characteristic features.

DOI
10.7498/aps.49.1550

Related papers

The Elementary Excitation in Spin Peierls System

Xu Jing

Using bosonization and quantum self-consistent method,the elementary excitation of Spin-Peierls(SP)system is studied. We calculate and discuss ground state and the one-particle excited state of the SP system. By analyzing the self-consistent equation of K, we obtain that the SP system exhibits two phases, i.e. gapful dimerized phase and gapless antiferromagnetic phase. The variation of the ground state and energy gap with frustration parameter has also been investigated.

Journal of Zhoukou Normal University•Jan 1, 2000•0 citations

Quantum lattice dynamical effects on the low-energy excitations in spin-Peierls systems

Xu Jing, Wang Zhi-Guo, Shi Yun-Long +3 more

Using the bosonization technique and Gaussian wave functional method, we investi gate the low-energy excitations of a spin-Peierls chain where the spins interact with quantum phonons. The results show that the energy gap of the one- and two- particle excitation states decrease gradually when spin-phonon coupling constant decreases or the phonon frequency increases. A quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase occurs at a nonzero critica l value of the spin-phonon coupling. Our results indicate that the two-particle excitation spectrum is much more sensitive to spin-phonon coupling constant than the one-particle excitation spectrum.

Acta Physica Sinica•Jan 1, 2004•2 citations

Elementary Excitation and Ground-State Properties of Dimerized XXZ Chain with Frustration

Xue‐Fan Jiang, Qing Jiang, D. Y. Xing

We employ bosonization technique and quantum self-consistent theory to study the elementary excitation and ground-state properties of a dimerized XXZ S = 1/2 antiferromagnetic chain with frustration. The ground-state energy and one-magnon excited energy gap are calculated for frustration α > αc(γ), where α = αc(γ) is a critical line of frustration as a function of anisotropy on which there is a transition into a spontaneously dimerized ground state. It is shown that the ground-state energy decreases and the excited energy gap increases with increasing either frustration or dimerization for an anisotropic chain. We find that the dimerization dependence of the ground-state energy for small dimerization obeys the power law only on α = αc(γ), whereas it becomes a linear law when frustration and anisotropy parameters are far away from the critical line in the gapful range. The behavior of spin correlation in the ground state is also discussed analytically, which decays exponentially indicating a singlet ground state with an excited gap.

physica status solidi (b)•Feb 1, 2002•1 citation

Excitation spectrum of the S=1/2 quantum spin ladder with frustration: Elementary quasiparticles and many-particle bound states

Valeri N. Kotov, Oleg P. Sushkov, R. Eder

The excitation spectrum of the two-chain $S=1/2$ Heisenberg spin ladder with additional second neighbor frustrating interactions is studied by a variety of techniques. A description, based on a mapping of the model onto a Bose gas of hard-core triplets is used to determine the one- and two-particle excitation spectra. We find that low-lying singlet and triplet bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by exact diagonalization and variational methods. We prove that the larger the number of bound particles the larger the binding energy. Thus the excitation spectrum has a complex structure and consists of elementary triplets and composite many-particle singlet and triplet bound states. The composite excitations mix strongly with the elementary ones in the coupling regime where quantum fluctuations are strong. The quantum phase transition, known to take place in this model at critical frustration, is interpreted as a condensation process of (infinitely) large many-particle bound states.

arXiv:cond-mat/9808169•Physical review. B, Condensed matter•Mar 1, 1999•65 citations

Analytical approach to dimerized and frustrated Heisenberg chains

Xue‐Fan Jiang, Haoxin Chen, D. Y. Xing +1 more

We present a self-consistent quantum-theoretical analysis of the ground-state energy and low-energy excitation spectrum of a dimerized and frustrated Heisenberg chain by the bosonization representation in the continuum-limit approach. The frustration effects on the ground-state energy and energy gap are investigated for α>αc where α is the frustration parameter and αc is its critical value, above which a frustration-induced energy gap is opened. It is shown that as α increases, the ground-state energy decreases and the energy gap increases. We find that the dimerization dependence of the ground-state energy and energy gap for small dimerization obeys the Cross-Fisher power law only at α = αc, but departs significantly from it when α>αc. The present results are in good agreement with numerical analyses from the density-matrix renormalization-group and exact diagonalization methods. The relevance of our calculated results to recent experiments on the spin-Peierls compounds CuGeO3 is also discussed.

Journal of Physics Condensed Matter•Jul 12, 2001•6 citations

Excitation spectra of the linear alternating antiferromagnet

Jill C. Bonner, Hendrik W. J. Blöte

The linear, spin-$\frac{1}{2}$, alternating Heisenberg chain has attracted theoretical and experimental attention from physical chemists for about two decades, particularly in relation to spin exciton theory and the properties of linear, exchange-coupled free radicals. The model is somewhat unfamiliar to physicists but has become of increasing interest recently, primarily because of its relation to spin-Peierls transition systems. A striking feature of this model is that it has so far proved resistant to any form of analytic attack. Existing theories are therefore all approximate, and are not in agreement with one another. In particular, there is disagreement about the existence of an energy gap in the excitation spectrum for nonzero alternation, such a gap being crucial to spin-Peierls theory and spin exciton theory. In this paper we employ the method which has so far proved more reliable than any other approximate technique, namely the method of extrapolating exact finite-chain calculations to the thermodynamic limit. Our study is an extension of earlier work in this direction, and focuses on the nature of the ground state and on low-lying excitations in general, and the existence and properties of the gap in particular. We introduce the features of the linear alternating antiferromagnet through an initial description of the spin-Peierls transition and with brief reference to organic free radicals and spin exciton theory. This is followed by a survey of existing approximate theories. Features of the excitation spectrum are discussed and finite-chain extrapolations for the ground-state energy and energy gap as a function of alternation are presented. Comparisons are made with similar procedures performed on exactly solvable models, as a test of the expected accuracy of the extrapolations. Excitation spectra for a variety of other alternating models, classical and quantum, are calculated and surveyed comparatively. An unusual variety of behavior is observed, with striking differences between quantum and classical systems. Finally, a detailed comparison is made between our results and those of other approximate methods, including the new quantum renormalization-group approach. Particular attention is paid to values for the $T=0$ spin-Peierls critical exponents.

Physical review. B, Condensed matter•Jun 1, 1982•157 citations
By using bosonization technique and quantum self-consistent theory, we study the low-energy excitations of a spin-Peierls system. The ground state, one-particle excited state, two-particle bound state are calculated, and it is shown, as the frustration increases, the energy of the ground state decreases while the energy gap of the one- and two-particle states increases. By analysing the asymototic behavior of the longitudinal spin correlation function, we obtain that the two-particle bound state has similar spin structures as those of the singlet ground state. Thus, we regard the bound state as a singlet state, which exists between the ground state and the two-particle continuous excited state. Our results are qualitatively in agreement with the experimental phenomena observed by Ain et al. It is shown that the existence of bound state is one of the spin-Peierls system's characteristic features.
Using the bosonization technique and Gaussian wave functional method, we investi gate the low-energy excitations of a spin-Peierls chain where the spins interact with quantum phonons. The results show that the energy gap of the one- and two- particle excitation states decrease gradually when spin-phonon coupling constant decreases or the phonon frequency increases. A quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase occurs at a nonzero critica l value of the spin-phonon coupling. Our results indicate that the two-particle excitation spectrum is much more sensitive to spin-phonon coupling constant than the one-particle excitation spectrum.
We employ bosonization technique and quantum self-consistent theory to study the elementary excitation and ground-state properties of a dimerized XXZ S = 1/2 antiferromagnetic chain with frustration. The ground-state energy and one-magnon excited energy gap are calculated for frustration α > αc(γ), where α = αc(γ) is a critical line of frustration as a function of anisotropy on which there is a transition into a spontaneously dimerized ground state. It is shown that the ground-state energy decreases and the excited energy gap increases with increasing either frustration or dimerization for an anisotropic chain. We find that the dimerization dependence of the ground-state energy for small dimerization obeys the power law only on α = αc(γ), whereas it becomes a linear law when frustration and anisotropy parameters are far away from the critical line in the gapful range. The behavior of spin correlation in the ground state is also discussed analytically, which decays exponentially indicating a singlet ground state with an excited gap.
The excitation spectrum of the two-chain S=1/2S=1/2S=1/2 Heisenberg spin ladder with additional second neighbor frustrating interactions is studied by a variety of techniques. A description, based on a mapping of the model onto a Bose gas of hard-core triplets is used to determine the one- and two-particle excitation spectra. We find that low-lying singlet and triplet bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by exact diagonalization and variational methods. We prove that the larger the number of bound particles the larger the binding energy. Thus the excitation spectrum has a complex structure and consists of elementary triplets and composite many-particle singlet and triplet bound states. The composite excitations mix strongly with the elementary ones in the coupling regime where quantum fluctuations are strong. The quantum phase transition, known to take place in this model at critical frustration, is interpreted as a condensation process of (infinitely) large many-particle bound states.
We present a self-consistent quantum-theoretical analysis of the ground-state energy and low-energy excitation spectrum of a dimerized and frustrated Heisenberg chain by the bosonization representation in the continuum-limit approach. The frustration effects on the ground-state energy and energy gap are investigated for α>αc where α is the frustration parameter and αc is its critical value, above which a frustration-induced energy gap is opened. It is shown that as α increases, the ground-state energy decreases and the energy gap increases. We find that the dimerization dependence of the ground-state energy and energy gap for small dimerization obeys the Cross-Fisher power law only at α = αc, but departs significantly from it when α>αc. The present results are in good agreement with numerical analyses from the density-matrix renormalization-group and exact diagonalization methods. The relevance of our calculated results to recent experiments on the spin-Peierls compounds CuGeO3 is also discussed.
The linear, spin-12\frac{1}{2}21​, alternating Heisenberg chain has attracted theoretical and experimental attention from physical chemists for about two decades, particularly in relation to spin exciton theory and the properties of linear, exchange-coupled free radicals. The model is somewhat unfamiliar to physicists but has become of increasing interest recently, primarily because of its relation to spin-Peierls transition systems. A striking feature of this model is that it has so far proved resistant to any form of analytic attack. Existing theories are therefore all approximate, and are not in agreement with one another. In particular, there is disagreement about the existence of an energy gap in the excitation spectrum for nonzero alternation, such a gap being crucial to spin-Peierls theory and spin exciton theory. In this paper we employ the method which has so far proved more reliable than any other approximate technique, namely the method of extrapolating exact finite-chain calculations to the thermodynamic limit. Our study is an extension of earlier work in this direction, and focuses on the nature of the ground state and on low-lying excitations in general, and the existence and properties of the gap in particular. We introduce the features of the linear alternating antiferromagnet through an initial description of the spin-Peierls transition and with brief reference to organic free radicals and spin exciton theory. This is followed by a survey of existing approximate theories. Features of the excitation spectrum are discussed and finite-chain extrapolations for the ground-state energy and energy gap as a function of alternation are presented. Comparisons are made with similar procedures performed on exactly solvable models, as a test of the expected accuracy of the extrapolations. Excitation spectra for a variety of other alternating models, classical and quantum, are calculated and surveyed comparatively. An unusual variety of behavior is observed, with striking differences between quantum and classical systems. Finally, a detailed comparison is made between our results and those of other approximate methods, including the new quantum renormalization-group approach. Particular attention is paid to values for the T=0T=0T=0 spin-Peierls critical exponents.