Critical lines and massive phases in quantum spin ladders with dimerization

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

doi:10.1103/physrevb.77.094415

Cited by 15 publications

(22 citation statements)

References 27 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%

“…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%

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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: Introductionmentioning

confidence: 99%

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

Self Cite

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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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“…Analytical methods have been applied to uncover this rich phase structure, some of them non-perturbative [1,6,7,8,9]. However, they are not sufficient to study with enough precision the whole range of coupling parameters entering in their quantum lattice Hamiltonians and, consequently, they have to be complemented with numerical studies [10,11,12,13], which sometimes modify the conclusions achieved with analytical methods, either quantitative and/or qualitatively.…”

Section: Introductionmentioning

confidence: 99%

Twisted-order parameter applied to dimerized ladders

Almeida¹,

Martín-Delgado²,

Sierra³

2008

J. Phys. A: Math. Theor.

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We apply the twisted order parameter (TOP) for dimerized quantum spin ladders to locate the critical phases that separate gapped phases representing quantum spin liquids of various types. Using the DMRG, method we find that the TOP is a good order parameter for these systems regardless the number of legs. As a check, we reproduce with DMRG and periodic boundary conditions the computations previously done with Quantum Montecarlo for one-dimensional S=1/2, S=1, S=3/2 and S=2 Heisenberg chains with alternating bonds.

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Critical lines and massive phases in quantum spin ladders with dimerization

Cited by 15 publications

References 27 publications

Berry phase investigation of spin-Sladders

Berry phase investigation of spin-Sladders

Valence bond solid state induced by impurity frustration inCr8Ni

Twisted-order parameter applied to dimerized ladders

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