scholarly journals Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes

2021 ◽  
Vol 103 (19) ◽  
Author(s):  
Tomonari Mizoguchi ◽  
Tohru Koma
Keyword(s):  
Transfer Matrix ◽  
Two Dimensional ◽  
Topological Semimetals

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

scholarly journals Films of rhombohedral graphite as two-dimensional topological semimetals

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Sergey Slizovskiy ◽  
Edward McCann ◽  
Mikito Koshino ◽  
Vladimir I. Fal’ko
Keyword(s):  
Thin Films ◽  
Anomalous Hall Effect ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Berry Curvature ◽  
Electrostatic Gating ◽  
Topological Semimetals ◽  
Intrinsic Magnetic Moment

AbstractTopologically non-trivial states appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the material’s transport characteristics. Here we consider thin films of rhombohedral graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimensional electron states with a large Berry curvature, accompanied by a giant intrinsic magnetic moment carried by electrons. The size of Berry curvature and magnetization in the vicinity of each valley can be controlled by electrostatic gating leading to a tuneable anomalous Hall effect and a peculiar structure of the two-dimensional Landau level spectrum.

scholarly journals Two-dimensional topological semimetals protected by symmorphic symmetries

2020 ◽  
Vol 101 (19) ◽  
Author(s):  
Wei Luo ◽  
Junyi Ji ◽  
Jinlian Lu ◽  
Xiuwen Zhang ◽  
Hongjun Xiang
Keyword(s):  
Two Dimensional ◽  
Topological Semimetals

scholarly journals A transfer matrix for the backbone exponent of two-dimensional percolation

2002 ◽  
Vol 35 (9) ◽  
pp. 2131-2144 ◽  
Author(s):  
Jesper Lykke Jacobsen ◽  
Paul Zinn-Justin
Keyword(s):  
Transfer Matrix ◽  
Two Dimensional
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