Identification of intrinsic gapped behavior in spin-1/2 ladder with staggered dimerization

Yao, K.L.; Ding, Lu

doi:10.1016/j.physa.2011.11.036

Cited by 6 publications

(8 citation statements)

References 33 publications

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“…6 In recent years the investigation of the topological properties of other models of quantum magnetism, in particular spin-1/2 ladders, has been a very active field of research. [7][8][9][10][11][12][13][14][15][16][17] A few years ago, Hatsugai proposed an alternative characterization of quantum magnets in terms of a Berry phase defined by twisting the XY components of the spin-spin interaction of one or several local bonds. 18,19 He showed that, if the system has time-reversal symmetry, this Berry phase is quantized and can only take the values 0 or π (mod 2π ), and that some phase transitions can be characterized by a change of Berry phase.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, in the modern language of topological matter, the ground state of the spin-1 chain is in a topologically non-trivial phase characterized by a string order parameter 5 and by spin-1/2 edge states 6 . In recent years, the investigation of the topological properties of other models of quantum magnetism, in particular spin-1/2 ladders, has been a very active field of research [7][8][9][10][11][12][13][14][15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

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Berry phase investigation of spin-Sladders

2013

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We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Berry phase investigation of spin-Sladders

2013

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“…Curiously enough, such tricky order parameter is given by a simple analytical expression from Eqs. (58,66).…”

Section: Region (C)mentioning

confidence: 99%

“…[61] The spin ladder is equivalent to an interacting fermionic model which is treated in this work within a Hartree-Fock mean-field approach. Such mean-field theory is known to be quite accurate even quantitatively for spin ladders [62][63][64][65], and was previously successfully applied to study the quantum phase transitions with nonlocal orders in the dimerized ladders [12,14,19,66,67].…”

Section: Introductionmentioning

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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“…Various properties of a wide range of different ladder models have been studied, like spin ladder systems with dimerization [35][36][37][38][39][40][41] , zig-zag ladders 23,[42][43][44][45] , mixed ladders [46][47][48][49][50] . A gapless phase has been found in two-leg zig-zag ladders with frustration by benefiting from exact diagonalization and density matrix renormalization group (DMRG) methods 23 .…”

Section: Introductionmentioning

confidence: 99%

Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study

Kanbur,

Polat,

Vatansever

2020

Preprint

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A two-leg quenched random bond disordered antiferromagnetic spin−1/2 Heisenberg ladder system is investigated by means of stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat take the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.

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Identification of intrinsic gapped behavior in spin-1/2 ladder with staggered dimerization

Cited by 6 publications

References 33 publications

Berry phase investigation of spin-Sladders

Berry phase investigation of spin-Sladders

Brane order and quantum magnetism in modulated anisotropic ladders

Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study

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