Twisted boundary conditions in cluster calculations of the optical conductivity in two-dimensional lattice models

1991 ◽  
Vol 44 (17) ◽  
pp. 9562-9581 ◽  
Author(s):  
Didier Poilblanc
Keyword(s):  
Boundary Conditions ◽  
Optical Conductivity ◽  
Lattice Models ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Cluster Calculations ◽  
Twisted Boundary Conditions

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

scholarly journals Twisted bulk-boundary correspondence of fragile topology

Science ◽  
2020 ◽  
Vol 367 (6479) ◽  
pp. 794-797 ◽  
Author(s):  
Zhi-Da Song ◽  
Luis Elcoro ◽  
B. Andrei Bernevig
Keyword(s):  
Boundary Conditions ◽  
Topological Insulator ◽  
Experimental Verification ◽  
Real Space ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Numbers ◽  
Boundary Correspondence ◽  
Topological States ◽  
Twisted Boundary Conditions

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

scholarly journals CONTINUOUS ABELIAN SANDPILE MODEL IN TWO DIMENSIONAL LATTICE

2011 ◽  
Vol 25 (32) ◽  
pp. 4709-4720 ◽  
Author(s):  
N. AZIMI-TAFRESHI ◽  
E. LOTFI ◽  
S. MOGHIMI-ARAGHI
Keyword(s):  
Boundary Conditions ◽  
Small Mass ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Model ◽  
Different Boundary Conditions ◽  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
General Properties ◽  
Abelian Sandpile

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.

OPTICAL CONDUCTIVITY OF TWO-DIMENSIONAL LATTICE

2008 ◽  
Vol 22 (06) ◽  
pp. 435-445 ◽  
Author(s):  
LEI XU ◽  
JUN ZHANG
Keyword(s):  
Optical Conductivity ◽  
Tight Binding ◽  
Two Dimensional ◽  
Energy Bands ◽  
Electron Model ◽  
Dimensional Lattice ◽  
Flux Parameter ◽  
Drude Weight ◽  
The Mean ◽  
Mean Kinetic Energy

We investigate the optical conductivity in the two-dimensional (2D) square and triangular tight-binding lattice-electron model with staggered magnetic flux (SMF). The SMF results in a two-sublattice system with two branches of energy bands in both cases, and even generates new flux-dependent optical properties. Results for the flux parameter dependence of the mean kinetic energy, the Drude weight and the optical conductivity are discussed in detail. A comparison between the two cases has been done.

scholarly journals CONTINUUM AND LATTICE OVERLAP FOR CHIRAL FERMIONS ON THE TORUS

1996 ◽  
Vol 11 (21) ◽  
pp. 3987-4003 ◽  
Author(s):  
C.D. FOSCO
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Effective Action ◽  
Lattice Spacing ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
The Real ◽  
Theory Result ◽  
Twisted Boundary Conditions ◽  
The Continuum

The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We first evaluate the continuum overlap, which is convergent and well-defined, and yields the correct string theory result for both the real and imaginary parts of the effective action. We then show that the lattice version of the overlap gives the continuum overlap results in the limit where the lattice spacing tends to zero, and that the subleading terms in that limit are irrelevant.

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