Phase diagram of the Heisenberg spin ladder with ring exchange

Gritsev, Vladimir; Normand, B.; Baeriswyl, D.

doi:10.1103/physrevb.69.094431

Cited by 42 publications

(49 citation statements)

References 54 publications

(106 reference statements)

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“…15 The ground state is the product of plaquette singlet states. 34 Moreover, through the duality transformation, 12 H DVC is mapped to the summation of S 2i,1 · S 2i,2 + S 2i+1,1 · S 2i+1,2 − S 2i,1 · S 2i+1,2 − S 2i,2 · S 2i+1,1 .…”

Section: Vector-chirality Phasementioning

confidence: 99%

“…11 Especially, the two-leg ladder model with the multiplespin exchange interactions has been studied extensively. [12][13][14][15][16][17][18][19] To clarify its rich phases, not only correlation functions corresponding to phases but also entanglement concurrence, 20 entanglement entropy, 21,22 and string order 14,23 are useful to characterize the phases. As such a novel order parameter, which is beyond the Ginzburg-Landau symmetry-breaking description, there is an order parameter based on the topological invariants corresponding to the topological order.…”

Section: Introductionmentioning

confidence: 99%

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Topological identification of a spin-12two-leg ladder with four-spin ring exchange

2009

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A spin-1 2 two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as localorder parameters. Reflecting local objects, nontrivial ͑͒ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

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Section: Vector-chirality Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

2009

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“…16). The model (1) is interesting in its own right and has been studied extensively over the years and its phase diagram [26][27][28][29][30] , ground-state-and dynamical properties 14,[31][32][33] , quantum phase transitions [34][35][36] , and entanglement properties [37][38][39] have been explored by both analytical and numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

2012

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We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hardcore bosons which treat the Néel and vector chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring-exchange. In particular, we derive the lowenergy effective actions which govern the physical properties of the rung-singlet and dominant vector chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.

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“…This description works well when the interchain exchange is much smaller than the exchange along the ladder. Then parameters m t , m s (masses of the triplet and the singlet Majorana fermions) are proportional to the linear combinations of the conventional J ⊥ and the four-spin J cycle exchange integrals [8], [9]:…”

Section: Double Chains the Case When Charge Gaps >> Than The Spin Onesmentioning

confidence: 99%

Zero-energy Majorana modes in spin ladders and a possible realization of the Kitaev model

Nersesyan

Tsvelik

2011

EPL

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We show that in double-chain Mott insulators (ladders), disordered alternating ionic potentials may locally destroy coherence of magnetic excitations and lead to the appearance of spontaneously dimerized islands inside the Haldane spin-liquid phase. We argue that a boundary between the dimerized and Haldane phases of a spin-1/2 ladder supports a localized zero-energy Majorana fermion mode. Based on these findings we suggest a realization of a generalized Kitaev model where Majorana fermions can propagate in more than one dimension.

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Phase diagram of the Heisenberg spin ladder with ring exchange

Cited by 42 publications

References 54 publications

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

Zero-energy Majorana modes in spin ladders and a possible realization of the Kitaev model

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