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

physica status solidi (b)

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

Xue‐Fan Jiang, Qing Jiang, D. Y. Xing

Published Feb 1, 2002• 1 citation
Publisher

Abstract

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.

DOI
10.1002/1521-3951(200202)229:3<1451::aid-pssb1451>3.0.co;2-u

Related papers

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

Temperature Dependence of Energy Gaps in Spin-1/2 Dimerized Heisenberg Chain

Jiang Xue-Fan, Xing Ding-Yu, Chen Hong

We present a method which combines a thermal coherent state approach with a self-consistent quantum theory to investigate the spin-1/2 dimerized antiferromagnetic Heisenberg chain. It is found that both excitation gaps between the ground state and two lowest excited modes, the triplet one-magnon excitation and the singlet two-magnon bound state decrease monotonically with increasing temperature. Our results are consistent with those obtained from the other approximations.

Chinese Physics Letters•Mar 26, 2002•2 citations

Temperature Dependence of Energy Gaps in Spin—1／2 Dimerized Heisenberg Chain

江学范, 陈鸿

We present a method which combines a thermal coherent state approach with a self-consistent quantum theory to investigate the spin-1/2 dimerized antiferromagnetic Heisenberg chain.It is found that both excitation gaps between the ground state and two lowest excited modes,the triplet one-magnon excitation and the singlet two-magnon bound state decrease monotonically with increasing temperature.Our results are consitent with those obtained from the other approximations.

Chinese Physics Letters•Jan 1, 2002•0 citations

Spectrum of elementary and collective excitations in the dimerized S=1/2 Heisenberg chain with frustration

Pavel V. Shevchenko, Valeri N. Kotov, Oleg P. Sushkov

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet $(S=0)$ and triplet $(S=1)$ modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.

arXiv:cond-mat/9901302•Physical review. B, Condensed matter•Aug 1, 1999•23 citations

Zigzag spin- S chain near the ferromagnet-antiferromagnet transition point

Д. В. Дмитриев, V. Ya. Krivnov, Johannes Richter

The properties of the ferromagnetic frustrated spin-$S$ one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for $s=1∕2$ are sufficiently strong to change the classical critical exponents, while for spin systems with $s\ensuremath{\geqslant}1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.

arXiv:cond-mat/0610103•Physical Review B•Jan 18, 2007•33 citations

Ground-state phase diagram of a spin- 12 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases

Shunsuke Furukawa, Masahiro Sato, Shigeki Onoda +1 more

The ground-state phase diagram of a spin-$\frac{1}{2}$ XXZ chain with competing ferromagnetic nearest-neighbor (${J}_{1}<0$) and antiferromagnetic second-neighbor (${J}_{2}>0$) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.

arXiv:1207.1059•Physical Review B•Sep 12, 2012•120 citations
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.
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.
We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0)(S=0)(S=0) and triplet (S=1)(S=1)(S=1) modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.
The properties of the ferromagnetic frustrated spin-SSS one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for s=1∕2s=1∕2s=1∕2 are sufficiently strong to change the classical critical exponents, while for spin systems with $s\ensuremath{\geqslant}1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.
The ground-state phase diagram of a spin-12\frac{1}{2}21​ XXZ chain with competing ferromagnetic nearest-neighbor (J1<0{J}_{1}<0J1​<0) and antiferromagnetic second-neighbor (J2>0{J}_{2}>0J2​>0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.