Phase diagram of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>two-leg spin ladder with staggered bond alternation

Okamoto, Ken‐ichi

doi:10.1103/physrevb.67.212408

Cited by 17 publications

(18 citation statements)

References 14 publications

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“…Later, a series of different approximate analytical studies [12], [13] have been favorable for the existence of a critical line in the simplest case of a 2-leg spin ladder with staggered dimerization. Also, some preliminary numerical methods with the Lanczos algorithm [14], [15] have shown support for this fact for ladders with small size. Despite these several studies, a complete nonperturbative numerical analysis of these staggered low dimensional quantum spin systems have remained as an open problem.…”

Section: Introductionmentioning

confidence: 86%

Critical lines and massive phases in quantum spin ladders with dimerization

Almeida¹,

Martín-Delgado²,

Sierra³

2008

Phys. Rev. B

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We determine the existence of critical lines in dimerized quantum spin ladders in their phase diagram of coupling constants using the finite-size DMRG algorithm. We consider both staggered and columnar dimerization patterns, and antiferromagnetic and ferromagnetic inter-leg couplings. The existence of critical phases depends on the precise combination of these patterns. The nature of the massive phases separating the critical lines are characterized with generalized string order parameters that determine their valence bond solid (VBS) content.

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Section: Introductionmentioning

confidence: 86%

Critical lines and massive phases in quantum spin ladders with dimerization

Almeida¹,

Martín-Delgado²,

Sierra³

2008

Phys. Rev. B

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“…4 and have been confirmed by subsequent numerical and analytical work. [5][6][7][8][9][10][11][12] The characterization of the unconventional quantum phases in such systems in terms of more exotic types of orders may ultimately help to uncover novel physics which lies beyond the Landau paradigm.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of critical properties and hidden orders in dimerized spin ladders

2011

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Dimerized antiferromagnetic spin-1 2 ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a nonlocal (hidden) string-order parameter, which is nonzero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground-state energies, energy gaps, and string-order parameters of dimerized two-and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents ν and β.

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“…Subtle interplay of relevant terms may result in that the dimerized two-(or three-) leg ladders made out of gapped spin chains, can be gapless. The criticality (gaplessness) in the dimerized two-and three-leg ladders was first conjectured in [4] and has been confirmed by subsequent numerical and analytical work [5][6][7][8][9][10][11][12][13][14][15][16][17]. The main interest in dimerized ladders comes from the real experiments on the spin-Peierls ladder-type compounds, see, e.g., [18], so the spin-Peierls transitions were analyzed in the ladder models, see, e.g., [15,19,20].…”

Section: Introductionmentioning

confidence: 71%

“…The phase diagram of the isotropic (γ = 0) dimerized ladder and quantum phase transitions, accompanied by non-local order parameters in this model, were actively g ( ) A studied in the literature [4][5][6][7][8][9][10][11][12][13][14][15]. The anisotropy (γ = 0) renders model's phase diagram richer: phases with nonlocal (brane) orders are found along with conventional antiferromagnetic phases.…”

Section: Spectra Phase Diagram and Dual Models A Staggered Laddermentioning

confidence: 99%

Brane order and quantum magnetism in modulated anisotropic ladders

Pandey¹,

Chitov²

2021

Preprint

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Two-leg spin-1 2 ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess non-local brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which can undergo the predicted quantum phase transitions with gap closures and distinct brane orders.

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Phase diagram of theS=12two-leg spin ladder with staggered bond alternation

Cited by 17 publications

References 14 publications

Critical lines and massive phases in quantum spin ladders with dimerization

Critical lines and massive phases in quantum spin ladders with dimerization

Numerical study of critical properties and hidden orders in dimerized spin ladders

Brane order and quantum magnetism in modulated anisotropic ladders

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