Topological identification of a spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math>two-leg ladder with four-spin ring exchange

Maruyama, Isao; Hirano, Takaaki; Hatsugai, Yasuhiro

doi:10.1103/physrevb.79.115107

Cited by 25 publications

(31 citation statements)

References 39 publications

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“…[15] The global Berry phase has been used as a topological index for the Hermitian Hamiltonian. [3,19] Here we find the gauge invariance of the complex Berry phase and global Berry phase for a generic non-Hermitian Hamiltonian and generalize the global Berry phase to identify the topological invariance for non-Hermitian Hamiltonian.…”

Section: Claim 33mentioning

confidence: 84%

Topological invariance and global Berry phase in non-Hermitian systems

Liang¹,

Huang²

2013

Phys. Rev. A

212

128

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Studying the topological invariance and Berry phase in non-Hermitian systems, we give the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance to non-Hermitian models. We find that Q can identify a topological invariance in two kinds of non-Hermitian models, two-level non-Hermitian Hamiltonian and bipartite dissipative model. For the bipartite dissipative model, the abrupt change of the Berry phase in the parameter space reveals quantum phase transition and relates to the exceptional points.These results give the basic relationships between the Berry phase, quantum and topological phase transitions.

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Section: Claim 33mentioning

confidence: 84%

Topological invariance and global Berry phase in non-Hermitian systems

Liang¹,

Huang²

2013

Phys. Rev. A

212

128

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“…19,20 The relevance of the four-spin cyclic exchange has also been reported [21][22][23][24][25][26][27][28][29] in the frame of inelastic neutron-scattering experiments for cuprates such as La 2 CuO 4 , La 6 The model (1) in the N = 2 case has been studied extensively over the years by means of different analytical and numerical approaches. [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] The zero-temperature phase diagram is rich and several exotic phases have been identified such as a scalar chirality phase which spontaneously breaks the time-reversal symmetry. 31 When J ⊥ > 0, the ring exchange destabilizes the well-known rung-singlet (RS) phase of the standard two-leg spin ladder and a staggered dimerization (SD) phase emerges.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions in multileg spin ladders with ring exchange

2013

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Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general N-leg spin ladder. We show by means of a low-energy approach that, depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)_N conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of Exact Diagonalization and Density Matrix Renormalization Group approaches for N \le 4

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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%

“…The 1/2-plateau phase appears in the applied magnetic field, which breaks most of the symmetry of the system. The ladder model itself has been studied extensively [12][13][14][15][16][17][18] and some of the studies shed light on the topological aspects of the ladder model [19][20][21], but the focus has mainly been on the case without magnetic * kariyado@rhodia.ph.tsukuba.ac.jp † hatsugai@rhodia.ph.tsukuba.ac.jp field. (Very recently, plateau phases at finite magnetization in spin chains have been studied using a SPT viewpoint in Ref.…”

Section: Introductionmentioning

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

Cited by 25 publications

References 39 publications

Topological invariance and global Berry phase in non-Hermitian systems

Topological invariance and global Berry phase in non-Hermitian systems

Quantum phase transitions in multileg spin ladders with ring exchange

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

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