Gapless points of dimerized quantum spin chains: Analytical and numerical studies

Chandra, Vinod; Sen, Diptiman; Surendran, Naveen

doi:10.1103/physrevb.74.184424

Cited by 11 publications

(36 citation statements)

References 23 publications

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“…The size of the plateaus can become nonmonotonic when increasing J ʈ + J ϫ and it is possible to obtain phase transitions inside the plateaus as already reported in Ref. 16 for the special case…”

Section: And Described By the Hamiltoniansupporting

confidence: 58%

“…15͒ as well as some models of spin-1 ladders. 16,17 In a combined analysis using perturbative methods and the density-matrix renormalization group ͑DMRG͒, we make exact predictions for the existence, the position and the sizes of these frustrationinduced plateaus ͑FP͒ in the strong-rung limit. We then extend the analysis beyond the strong-rung limit and identify an intermediate regime in which additional features, i.e., jumps in the magnetization curves and phase transitions inside the plateaus, are realized and compared to recent findings for particular values of the interactions.…”

Section: A Motivationmentioning

confidence: 99%

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Frustration-induced plateaus inS≥12Heisenberg spin ladders

Michaud

Coletta²,

Manmana³

et al. 2010

Phys. Rev. B

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We study the T = 0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin S. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins S and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for S Յ 2. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

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Section: And Described By the Hamiltoniansupporting

confidence: 58%

Section: A Motivationmentioning

confidence: 99%

Frustration-induced plateaus inS≥12Heisenberg spin ladders

Michaud

Coletta²,

Manmana³

et al. 2010

Phys. Rev. B

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“…It is worthy of notice that it is not possible to find the ground state outside the boundaries (22), (24), (25) using the variational principle. However, it is shown in the appendix that the bond configuration, which corresponds to the ground state, cannot exceed period two.…”

Section: Ground-state Phase Diagram In a Non-zero Fieldmentioning

confidence: 99%

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Verkholyak¹,

Strečka²

2012

J. Phys. A: Math. Theor.

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Abstract. Ground-state behaviour of the frustrated quantum spin-1 2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed to the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bondstate representation or the unitary transformation. It is shown that the ground state of the Heisenberg-Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the 'classical' Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal-transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin-spin correlations.

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“…We also note that the models under considerations are known as models with local conservation laws, see Refs. 20,21,[23][24][25][26]28,29. On the other hand, these models belong to a class of systems which support localized-magnon states. 8,[11][12][13] The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayers=12Heisenberg antiferromagnets

Derzhko

Krokhmalskii

Richter³

2010

Phys. Rev. B

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Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class. 1 2 J (a) J 1 2 J J (b) FIG. 1: (Color online) Lattices considered in this paper: (a) the frustrated two-leg ladder and (b) the frustrated bilayer. The vertical bonds have the strength J2 > 0 whereas all other bonds have the strength J1 > 0.

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Gapless points of dimerized quantum spin chains: Analytical and numerical studies

Cited by 11 publications

References 23 publications

Frustration-induced plateaus inS≥12Heisenberg spin ladders

Frustration-induced plateaus inS≥12Heisenberg spin ladders

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayers=12Heisenberg antiferromagnets

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