Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

Uhrig, Götz S.; Schönfeld, Friedhelm; Laukamp, Markus; Dagotto, Elbio

doi:10.1007/s100510050589

Cited by 48 publications

(83 citation statements)

References 41 publications

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“…This needs to be further addressed. The picture is much clearer in the soliton language, as one might expect: at small δ, there is a discrete spectrum of s −s bound states confined by a linear potential, which becomes continuous as δ → 0 and the confining potential vanishes [5,6,8]. Another puzzle is the crossing of energy levels.…”

Section: Conclusion and Discussionmentioning

confidence: 94%

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Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

et al. 2001

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We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop series expansions for bound state energies in various sectors, which can be extrapolated using standard methods to cases where the external bond-alternation goes to zero. We study the properties of singlet and triplet bound states in the latter limit and suggest a crucial role for the bound states in the unbinding of triplets and deconfinement of spin-half excitations.

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Section: Conclusion and Discussionmentioning

confidence: 94%

“…An explicit bond-alternating term in the Hamiltonian can be motivated as a mean-field representation of the inter-chain elastic couplings [5]. Uhrig et al [6] and Affleck and collaborators [7] have studied the confinement transition for the soliton-antisoliton pairs when such a term is added to the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

et al. 2001

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“…For any infinitesimal dimerization confinement occurs: Bound states of two spinon with total spin S = 1, called triplon, occur and constitute the elementary excitations [5][6][7][8][9][10] . In higher dimensions, the convential scenario is the occurrence of phases with long range magnetic order.…”

Section: Introductionmentioning

confidence: 99%

From gapped excitons to gapless triplons in one dimension

2015

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Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.

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“…Multi-spinons or multi-magnons contributions have recently been shown to be relevant in the spectral weight of several dynamical structure factors [24,25,26]. At the MG point, variational methods have been used to tackle the dispersion relation [27,28,29,30,31,32,33,34,35]. Working in the dimer basis gave a good account for the shape of the dispersion relation, with in particular the explanation for a triplet bound-state [27] close to K = π/2.…”

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confidence: 99%

Spinon excitation spectra of the J1-J2 chain from analytical calculations in the dimer basis and exact diagonalization

Lavarélo

Roux

2014

Eur. Phys. J. B

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Abstract. The excitation spectrum of the frustrated spin-1/2 Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at J2 = 0.25J1 and an onset of incommensurability in the dispersion relation at J2 = 9/17J1 [as in S. Brehmer et al., J. Phys.: Condens. Matter 10, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture. Frustration in antiferromagnetic magnets is one of the key ingredient to stabilize exotic phases [1]. In onedimension, where quantum fluctuations destroy the Néel order, a next-nearest neighbor coupling is known to bring two main features. There is first a transition from the quasi-long range ordered phase to a gapped phase which order parameter is the dimerization, breaking translational invariance. The second is the onset of incommensurability in the spin correlations and dispersion relation of elementary excitations. The J 1 -J 2 frustrated chain model is thus a paradigmatic model for quantum magnetism which has been widely studied and from which stemmed the physics of valence bond solid phases. PACSWe start by recalling known results on the frustrated spin-1/2 chain Hamiltonian which readsin which J 1,2 > 0 are antiferromagnetic couplings and S i are spin-1/2 operators. L denotes the length of the chain and periodic or open boundary conditions can be used.The phase transition to a dimerized state can be understood by bosonization arguments, leading to a KosterlitzThouless type of transition [2,3,4]. The transition point can be efficiently determined by level spectroscopy [5] and is found to be located at J 2 /J 1 0.241167 [3,5,6]. One peculiarity of the transition is the disappearance of logarithmic corrections associated with SU(2) symmetry right at the critical point [6]. Another way to understand the opening of the gap and the onset of a dimerized phase is to start the bosonization from the limit of two chains coupled in a zig-zag geometry [7], ie. the J 2 J 1 limit. Then, the gap is shown to decay exponentially with J 2 /J 1 , so as the dimerization. Between both regimes, the gap and dimerization curves display a intermediate maximum (not at the same location for both quantity) which is captured by numerics [3,7]. Deep in the dimerized phase, the two degenerate ground-states in the thermodynamical limit are well pictured by the Majumdar-Ghosh (MG) state which is a product of decoupled dimers on bonds |MG = | , where dimers are represented by | = 1 √ 2 (|↑↓ − |↓↑ ) and an even length is assumed. Actually, for the special value J 2 = J 1 /2, this MG state is the exact ground-state of the...

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Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

Cited by 48 publications

References 41 publications

Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

From gapped excitons to gapless triplons in one dimension

Spinon excitation spectra of the J1-J2 chain from analytical calculations in the dimer basis and exact diagonalization

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