Twisted-order parameter applied to dimerized ladders

Almeida, J. R. L. de; Martín-Delgado, M. A.; Sierra, Germȧn

doi:10.1088/1751-8113/41/48/485301

Cited by 12 publications

(9 citation statements)

References 39 publications

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“…As we shall see, the phase transitions of the dimerized spin chains disappear before reaching the spin ladder geometry, in agreement with previous results, 7,8,[10][11][12]15,27 but some traces of these phase transitions can still be found in the rung Berry phases of the ladder, suggesting the presence of a series of 2S crossovers in spin-S ladders.…”

Section: Introductionsupporting

confidence: 93%

“…In this paper, one of our goals is to clarify the difference between spin ladders and dimerized spin chains by a systematic investigation of different Berry phases in a model that interpolates between them. As we shall see, the phase transitions of the dimerized spin chains disappear before reaching the spin ladder geometry, in agreement with previous results 7,8,[10][11][12]15,27 , but some traces of these phase transitions can still be found in the rung Berry phases of the ladder, suggesting the presence of a series of 2S cross-overs in spin-S ladders.…”

Section: Introductionsupporting

confidence: 92%

“…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: Introductionsupporting

confidence: 93%

Section: Introductionsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Berry phase investigation of spin-Sladders

2013

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“…General (m, n)-VBS states belong to a class of spin liquids which are known to possess an special hidden order that can be identified by a particular non-local order parameter called the string order parameter (SOP) [22,23,24,25,26,27]. This order parameter has proved itself extremely successful in the task of characterizing diverse kinds of such states, both in the pure one dimensional cases and also in less trivial systems such as ladders [25], [27]. We shall see that this parameter also allows us to characterize the Cr8Ni ground state.…”

Section: Figmentioning

confidence: 99%

Valence bond solid state induced by impurity frustration inCr8Ni

2009

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We provide a physically meaningful picture of the nature of the ground state of the Cr8Ni compound in the regime where it is a spin singlet. According to this picture, the anisotropy of the N i atom in the Cr ring induces a dimerization in the molecule that makes the ground state to stabilize in a Valence Bond Solid phase of virtual spins. We characterize rigorously this phase by means of a particular non-local order parameter denoted the generalized string order parameter. In the completely antiferromagnetic regime, the system becomes frustrated. We have performed a numerical real-time evolution study of the correlations between the spin of the N i impurity and the rest of the spins in order to show the reaction of the system under this frustration. We provide results that manifestly show the agreement with the Valence Bond Solid picture introduced.

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0- and 2/3-magnetization plateaus in three-leg antiferromagnetic Heisenberg spin-1/2 ladders with leg-dimerization

Wang

et al. 2014

Physics Letters A

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Twisted-order parameter applied to dimerized ladders

Cited by 12 publications

References 39 publications

Berry phase investigation of spin-Sladders

Berry phase investigation of spin-Sladders

Valence bond solid state induced by impurity frustration inCr8Ni

0- and 2/3-magnetization plateaus in three-leg antiferromagnetic Heisenberg spin-1/2 ladders with leg-dimerization

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