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/9907303 · Physical review. B, Condensed matter

Fate of spinons in spontaneously dimerized spin- 12 ladders

Dave Allen, Fabian H. L. Eßler, A. A. Nersesyan

Published Apr 1, 2000• 67 citations
arXivHTMLPDF

Abstract

We study a weakly coupled, frustrated two-leg spin-1/2 Heisenberg ladder. For vanishing coupling between the chains, elementary excitations are deconfined, gapless spin-1/2 objects called spinons. We investigate the fate of spinons for the case of a weak interchain interaction. We show that despite a drastic change in ground state, which becomes spontaneously dimerized, spinons survive as elementary excitations but acquire a spectral gap. We furthermore determine the exact dynamical structure factor for several values of momentum transfer.

DOI
10.1103/physrevb.61.8871

Related papers

Dimerization process and elementary excitations in spin–Peierls chains coupled by frustrated interactions

Diego Mastrogiuseppe, C. J. Gazza, A. Dobry

We consider the ground state and the elementary excitations of an array of spin-Peierls chains coupled by elastic and magnetic interactions. It is expected that the effect of the magnetic interchain coupling will be to reduce the dimerization amplitude and that of the elastic coupling will be to confine the spin one-half solitons corresponding to each isolated chain. We show that this is the case when these interactions are not frustrated. On the other hand, in the frustrated case we show that the amplitude of dimerization in the ground state is independent of the strength of the interchain magnetic interaction in a broad range of values of this parameter. We also show that free solitons could be the elementary excitations when only nearest neighbor interactions are considered. The case of an elastic interchain coupling is analyzed on a general energetic consideration. To study the effect of the magnetic interchain interaction the problem is simplified to a two-leg ladder which is solved using DMRG calculations. We show that the deconfinement mechanism is effective even with a significantly strong antiferromagnetic interchain coupling.

arXiv:0707.0422•Journal of Physics Condensed Matter•Mar 13, 2008•4 citations

Dynamical transition from triplets to spinon excitations: A series expansion study of the J1−J2−δ spin- 12 chain

Rajiv R. P. Singh, Zheng Weihong

We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions ${J}_{1}(1+\ensuremath{\delta})$ and ${J}_{1}(1\ensuremath{-}\ensuremath{\delta})$ and a uniform second neighbor interaction ${J}_{2}=y(1\ensuremath{-}\ensuremath{\delta})$ by series expansions around the limit of decoupled dimers $(\ensuremath{\delta}=1).$ By extrapolating to $\ensuremath{\delta}=0$ and tuning y, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line $y=0.5,$ $0<~\ensuremath{\delta}<~1,$ where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights, and wave vector dependent static susceptibility along this line. It is well known that as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}0,$ the spin gap is still nonzero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin susceptibility changes from a simple pole at imaginary wave vectors to a branch cut at the transition.

arXiv:cond-mat/9811028•Physical review. B, Condensed matter•Apr 15, 1999•21 citations

Dynamical central peak and spinon deconfinement in frustrated spin chains

J. Kokalj, Peter Prelovšek

Studying the dynamical spin structure factor in frustrated spin chains with spontaneously dimerized ground state we show that besides the gapped spin-wave excitations there appears at finite temperatures also a sharp central peak. The latter can be attributed to deconfined spinons, accounted well within the variational approach. The central peak remains well pronounced within the local spin dynamics and may be relevant for experiments on materials with one-dimensional frustrated spin chains.

arXiv:1003.4232•Physical Review B•Aug 24, 2010•4 citations

Spin-Liquid versus Dimerized Ground States in a Frustrated Heisenberg Antiferromagnet

Luca Capriotti, Douglas J. Scalapino, Steven R. White

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.

arXiv:cond-mat/0404085•Physical Review Letters•Oct 20, 2004•35 citations

Phase Diagram of an Asymmetric Spin Ladder

Shu Chen, H. Büttner, Johannes Voit

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.

arXiv:cond-mat/0106651•Physical Review Letters•Aug 6, 2001•30 citations

Spinon confinement: Dynamics of weakly coupled Hubbard chains

Marcin Raczkowski, Fakher F. Assaad

Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at $T=0$. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.

arXiv:1306.5775•Physical Review B•Aug 21, 2013•24 citations
We study a weakly coupled, frustrated two-leg spin-1/2 Heisenberg ladder. For vanishing coupling between the chains, elementary excitations are deconfined, gapless spin-1/2 objects called spinons. We investigate the fate of spinons for the case of a weak interchain interaction. We show that despite a drastic change in ground state, which becomes spontaneously dimerized, spinons survive as elementary excitations but acquire a spectral gap. We furthermore determine the exact dynamical structure factor for several values of momentum transfer.
We consider the ground state and the elementary excitations of an array of spin-Peierls chains coupled by elastic and magnetic interactions. It is expected that the effect of the magnetic interchain coupling will be to reduce the dimerization amplitude and that of the elastic coupling will be to confine the spin one-half solitons corresponding to each isolated chain. We show that this is the case when these interactions are not frustrated. On the other hand, in the frustrated case we show that the amplitude of dimerization in the ground state is independent of the strength of the interchain magnetic interaction in a broad range of values of this parameter. We also show that free solitons could be the elementary excitations when only nearest neighbor interactions are considered. The case of an elastic interchain coupling is analyzed on a general energetic consideration. To study the effect of the magnetic interchain interaction the problem is simplified to a two-leg ladder which is solved using DMRG calculations. We show that the deconfinement mechanism is effective even with a significantly strong antiferromagnetic interchain coupling.
We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions ${J}_{1}(1+\ensuremath{\delta})$ and ${J}_{1}(1\ensuremath{-}\ensuremath{\delta})$ and a uniform second neighbor interaction ${J}_{2}=y(1\ensuremath{-}\ensuremath{\delta})$ by series expansions around the limit of decoupled dimers $(\ensuremath{\delta}=1).$ By extrapolating to $\ensuremath{\delta}=0$ and tuning y, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line y=0.5,y=0.5,y=0.5, $0<~\ensuremath{\delta}<~1,$ where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights, and wave vector dependent static susceptibility along this line. It is well known that as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}0,$ the spin gap is still nonzero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin susceptibility changes from a simple pole at imaginary wave vectors to a branch cut at the transition.
We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.
We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.
Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at T=0T=0T=0. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.