Random network models and quantum phase transitions in two dimensions

Krämer, B.; Ohtsuki, Tomi; Kettemann, Stefan

doi:10.1016/j.physrep.2005.07.001

Cited by 180 publications

(245 citation statements)

References 336 publications

(734 reference statements)

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“…with the critical index, ν ≈ 2.33 [32,50]. The critical quantum Hall regime can be studied numerically within the Hamiltonian, (19) with the Peierls phase, φ = B(ea)…”

Section: Critical Quantum Hall Regimementioning

confidence: 99%

Numerical analysis of the Anderson localization

Markoš¹

2006

Acta Physica Slovaca. Reviews and Tutorials

135

242

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The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electronelectron interaction and incoherent scattering are discussed in the paper.

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“…with the critical index, ν ≈ 2.33 [32,50]. The critical quantum Hall regime can be studied numerically within the Hamiltonian, (19) with the Peierls phase, φ = B(ea)…”

Section: Critical Quantum Hall Regimementioning

confidence: 99%

Numerical analysis of the Anderson localization

Markoš¹

2006

Acta Physica Slovaca. Reviews and Tutorials

135

242

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“…An inclusion of the next and the next nearest neighbor magnetic dipolar couplings imposes so-called two-in two-out ice rule for each vertex, which has been experimentally observed in a patterned ferromagnetic film. Using the transfer matrix method, [34][35][36] we first calculated the localization length of a single-particle eigenstate of a corresponding generalized eigenvalue problem with the randomness. Due to the bosonic nature, the eigenvalue problem takes a form of H BdG |φ ≡ σ 3 |φ E,…”

mentioning

confidence: 99%

Integer quantum magnon Hall plateau-plateau transition in a spin-ice model

Ohtsuki

Shindou

2016

Phys. Rev. B

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Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands under an out-of-plane field. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same universality class as that in the quantum Hall transition. We characterize thermal magnon Hall conductivity in disordered quantum magnon Hall system in terms of robust chiral edge magnon transport. PACS numbers:Bosonic analogue of integer quantum Hall states have been proposed in a number of quasi-particle boson systems with broken time-reversal symmetry such as photon, 1-6 phonon, 7 exciton, 8 exciton-polariton, 9 triplon, 10 magnon 11-19 and surface magnon-polariton. 20 Typically, their quasi-particle excitations have extended bulk bands with topological integers and topological edge modes whose chiral dispersions cross band gaps among these bulk bands. Due to its chiral (unidirectional) nature, a quasi-particle boson flow along the edge mode is believed to be robust against generic elastic backward scatters, fostering a rich prospect of their future applications. [1][2][3][4][5][6][7][8][9][11][12][13]20 On the one hand, these bosonic systems often break conservation of the quasi-particle number even at the level of respective quadratic Hamiltonian. 8,9,[11][12][13][14][15][16]19,[21][22][23][24][25][26][27] Thereby, one naturally wonders if the quasi-particle flow along the topological edge modes is still robust against such particle-number-nonconserving perturbations or not. In other words, one may raise a question whether two quantum Hall regimes with different Chern integers are topologically distinguishable even in the absence of the U(1) symmetry associated with the quasi-particle number conservation.In this rapid communication, we study effects of generic disorder potentials in a simplest spin model in a quantum magnon Hall regime. Our numerical results and the following argument clarify that, even without the explicit U(1) symmetry at the Hamiltonian level, the topological magnon edge mode provides a robust quantized magnon conductance and therefore quantum magnon Hall regimes with different topological integers are always distinguished by a quantum critical point with delocalized bulk magnon band. Thermal conductance distributions calculated at the critical point clearly shows that the quantum critical point belongs to the same universality class as the two-dimensional integer quantum Hall plateau-plateau transition. Based on these knowledge, we give a generic expression for the thermal Hall conductivity in disordered integer quantum bosonic Hall systems from edge transport picture.We study spin excitations in a square-lattice spin ice model 28-31 under out-of-plane Zeeman field H Z ;

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“…If these phases satisfy the criterion described above, then they are topologically distinct as long as the common U (1) symmetry G is preserved; therefore, there is a sharp phase transition between the two phases, even in the presence of interactions and disorder. The transport near the transition is then described in terms of percolation of the domain walls between the two phases [42][43][44][45] .…”

Section: Discussion and Relation To Experimentsmentioning

confidence: 99%

Spontaneous layer polarization and conducting domain walls in the quantum Hall regime of bilayer graphene

2015

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Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor ν = 2, domains walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

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Random network models and quantum phase transitions in two dimensions

Cited by 180 publications

References 336 publications

Numerical analysis of the Anderson localization

Numerical analysis of the Anderson localization

Integer quantum magnon Hall plateau-plateau transition in a spin-ice model

Spontaneous layer polarization and conducting domain walls in the quantum Hall regime of bilayer graphene

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