Multifractal wave functions in three-dimensional systems without time-reversal symmetry

1997 ◽  
Vol 56 (3) ◽  
pp. 975-978 ◽  
Author(s):  
Takamichi Terao
Keyword(s):  
Time Reversal ◽  
Three Dimensional ◽  
Wave Functions ◽  
Time Reversal Symmetry

Operators, Matrix Elements, and Wave Functions under Time-Reversal Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Quantum Chemistry ◽  
Time Reversal ◽  
Relativistic Quantum ◽  
Spin Symmetry ◽  
Computational Effort ◽  
Wave Functions ◽  
Time Reversal Symmetry ◽  
Molecular Systems ◽  
Self Consistent Field ◽  
Relativistic Quantum Chemistry

We now take on the task of developing the theory and methods for a relativistic quantum chemistry. The aim is to arrive at a qualitative as well as a quantitative understanding of the relativistic effects in molecules. We must be able to predict the effects of relativity on the wave functions and electron densities of molecules, and on the molecular properties arising from these. And we must develop methods and algorithms that enable us to calculate the properties and interactions of molecules with an accuracy comparable to that achieved for lighter systems in a nonrelativistic framework. Parts of this development follow fairly straightforwardly from our considerations of the atomic case in part II, but molecular systems represent challenges of their own. This is particularly true for the computational techniques. From the nonrelativistic experience we know that present-day quantum chemistry owes much of its success to the enormous effort that has gone into developing efficient methods and algorithms. This effort has yielded powerful tools, such as the use of basis-set expansions of wave functions, the exploitation of molecular symmetry, the description of correlation effects by calculations beyond the mean-field approximation, and so on. In developing a relativistic quantum chemistry, we must be able to reformulate these techniques in the new framework, or replace them by more suitable and efficient methods. In nonrelativistic theory, spin symmetry provides one of the biggest reductions in computational effort, such as in the powerful and elegant Graphical Unitary Group Approach (GUGA) for configuration interaction (CI) calculations (Shavitt 1988). For relativistic applications, time-reversal symmetry takes the place of spin symmetry, and this chapter is devoted to developing a formalism for efficient incorporation of this symmetry in our theory and methods. Time-reversal symmetry includes the spin symmetry of nonrelativistic systems, but there are significant differences from spin symmetry for systems with a Hamiltonian that is spin-dependent. The development of techniques that incorporate time-reversal symmetry presented here are primarily aimed at four-component calculations, but they are equally applicable to two-component calculations in which the spin-dependent operators are included at the self-consistent field (SCF) stage of a calculation.

Matrices and Wave Functions under Double-Group Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Time Reversal ◽  
Point Group ◽  
Computational Effort ◽  
Wave Functions ◽  
Group Symmetry ◽  
Time Reversal Symmetry ◽  
Point Group Symmetry ◽  
Matrix Elements ◽  
Double Group

Symmetry is one of the most versatile theoretical tools of physics and chemistry. It provides qualitative insight into the wave functions and properties of systems, and it has also been used successfully to obtain great savings in computational efforts. In the preceding chapter we examined time-reversal symmetry, and now we turn to the more familiar point-group symmetry. We show how relativity requires special consideration and extensions of the concepts developed for the nonrelativistic case, and how time-reversal symmetry and double-group symmetry are connected. Although the techniques that incorporate double-group symmetry presented here are primarily aimed at four-component calculations, they are equally applicable to two-component calculations in which the spin-dependent operators are included at the SCF stage of a calculation. In the preceding chapter, we have shown how the use of time-reversal symmetry can lead to considerable reduction in the number of unique matrix elements that appear in the operator expressions. However, we are also interested in the overall structure of the matrices of the operators. In particular, we are interested in possible block structures, where classes of matrix elements may be set to zero a priori. If the matrices can be cast in block diagonal form, we may save on storage as well as computational effort in solving eigenvalue problems, for example. Matrix blocking will already be effected by the point-group symmetry of the molecule.

scholarly journals The Casimir Effect in Topological Matter

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 237
Author(s):  
Bing-Sui Lu
Keyword(s):  
Time Reversal ◽  
Casimir Effect ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Mutual Orientation ◽  
Electromagnetic Properties ◽  
Time Reversal Symmetry ◽  
Electronic Band ◽  
Chern Insulators ◽  
Work Done

We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization.

scholarly journals Topological thermal Hall effect due to Weyl magnons

2018 ◽  
Vol 96 (11) ◽  
pp. 1216-1223 ◽  
Author(s):  
S.A. Owerre
Keyword(s):  
Hall Effect ◽  
Time Reversal ◽  
Low Temperatures ◽  
Three Dimensional ◽  
Zero Magnetic Field ◽  
Time Reversal Symmetry ◽  
Frustrated Magnets ◽  
Berry Curvature ◽  
Theoretical Evidence ◽  
Distribution Distance

We present the first theoretical evidence of zero magnetic field topological (anomalous) thermal Hall effect due to Weyl magnons in stacked noncoplanar frustrated kagomé antiferromagnets. The Weyl magnons in this system result from macroscopically broken time-reversal symmetry by the scalar spin chirality of noncoplanar chiral spin textures. Most importantly, they come from the lowest excitation, therefore they can be easily observed experimentally at low temperatures due to the population effect. Similar to electronic Weyl nodes close to the Fermi energy, Weyl magnon nodes at the lowest excitation are the most important. Indeed, we show that the topological (anomalous) thermal Hall effect in this system arises from nonvanishing Berry curvature due to Weyl magnon nodes at the lowest excitation, and it depends on their distribution (distance) in momentum space. The present result paves the way to directly probe low excitation Weyl magnons and macroscopically broken time-reversal symmetry in three-dimensional frustrated magnets with the anomalous thermal Hall effect.

scholarly journals Electron hydrodynamics in anisotropic materials

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Georgios Varnavides ◽  
Adam S. Jermyn ◽  
Polina Anikeeva ◽  
Claudia Felser ◽  
Prineha Narang
Keyword(s):  
Flow Pattern ◽  
Time Reversal ◽  
Large Scale ◽  
Three Dimensional ◽  
Anisotropic Materials ◽  
Three Dimensions ◽  
Time Reversal Symmetry ◽  
Classical Fluids ◽  
Large Scale Flow ◽  
Breaking Time

Abstract Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

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