Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchanges

Hikihara, Takashi; Yamamoto, Shoji

doi:10.1143/jpsj.77.014709

Cited by 14 publications

(30 citation statements)

References 64 publications

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“…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%

“…The other is that to the dominant collinear spin phase, which connects to the dominant vector-chirality phase through crossover at a self-dual point. 17 These two phases are the singlet phases with shortrange order and have dominant correlation of collinear spin and vector chirality, respectively. The rung-singlet phase includes the spin ladder with only two-spin exchange interactions and the dominant vector-chirality phase includes that with only four-spin exchange interactions.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2009

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“…58 Since the pure ring-exchange model does not exhibit such a symmetry breaking, 54 and because the most general spin ladder Hamiltonian contains too many parameters, we have used the previous variational analysis as a guide.…”

Section: B Numerical Resultsmentioning

confidence: 99%

“…54 As in the above cases, we carry out gradient expansion and the subsequent Gaussian integration over l Ω , l φ to obtain the non-linear sigma model (49) with different coupling constants (see Eq. (A16)).…”

Section: B Continuum Limitmentioning

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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“…Although the plateau phase under consideration can be mapped to the zero magnetization phase in the XXZ chain in the strong rung coupling limit, the fractional quantization is not expected in the XXZ chain since it does not admit the diagonal edge. is induced by a ring exchange [43,48], which is written as [19,20,35,43,49]…”

Section: Symmetry-breaking Boundary and Fractional Quantization Ofmentioning

confidence: 99%

Topological order parameters of the spin-12dimerized Heisenberg ladder in magnetic field

Kariyado

Hatsugai

2015

Phys. Rev. B

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Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated, focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry-protected topological phase supported by the spatial inversion symmetry. The Z 2 Berry phase associated with a symmetry-respecting boundary and quantized into 0 and π is used as a symmetry-protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry-breaking boundary is considered. Then, we observe a different type of quantization of the Berry phase, i.e., a quantization into ±π/2 of the Berry phase. In this case, the bulk-edge correspondence is also different, namely, there emerge "polarized" edge states for the case with ±π/2 quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry-phase-based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD.

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Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchanges

Cited by 14 publications

References 64 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

Topological order parameters of the spin-12dimerized Heisenberg ladder in magnetic field

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