The topological basis expression of four-qubit XXZ spin chain with twist boundary condition

2013 ◽  
Vol 12 (7) ◽  
pp. 2417-2426
Author(s):  
Guijiao Du ◽  
Kang Xue ◽  
Chengcheng Zhou ◽  
Chunfang Sun ◽  
Gangcheng Wang
Keyword(s):  
Boundary Condition ◽  
Spin Chain ◽  
Twist Boundary

scholarly journals Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

2018 ◽  
Vol 936 ◽  
pp. 501-519 ◽  
Author(s):  
Zhirong Xin ◽  
Yi Qiao ◽  
Kun Hao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
Boundary Energy ◽  
Antiperiodic Boundary Condition

scholarly journals Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Zhirong Xin ◽  
Yusong Cao ◽  
Xiaotian Xu ◽  
Tao Yang ◽  
Junpeng Cao ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Ground State Energy ◽  
Ground State ◽  
Spin Chain ◽  
State Energy ◽  
Elementary Excitations ◽  
Antiperiodic Boundary Condition ◽  
Bethe Ansatz Solution

Abstract Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$$ \frac{1}{2} $$ 1 2 XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter ηm,l, at which the associated inhomogeneous T − Q relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary η with O(N−2) corrections for a large N possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

scholarly journals Correlation functions of the XXZ spin chain with the twisted boundary condition

2020 ◽  
Vol 61 (3) ◽  
pp. 033502
Author(s):  
Yi Qiao ◽  
Zhirong Xin ◽  
Xiaotian Xu ◽  
Kun Hao ◽  
Tao Yang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Correlation Functions ◽  
Spin Chain ◽  
Twisted Boundary Condition

Structure and migration of planar defects in crystals observed in atomic scale

1978 ◽  
Vol 36 (1) ◽  
pp. 284-285 ◽  
Author(s):  
H. Hashimoto ◽  
Y. Sugimoto ◽  
Y. Takai ◽  
H. Endoh
Keyword(s):  
Electron Microscope ◽  
Rotation Angle ◽  
Crystal Surface ◽  
Electron Gun ◽  
Atomic Scale ◽  
Present Observation ◽  
Twist Boundary ◽  
Optical Magnification ◽  
Zinc Crystal ◽  
And Migration

As was demonstrated by the present authors that atomic structure of simple crystal can be photographed by the conventional 100 kV electron microscope adjusted at “aberration free focus (AFF)” condition. In order to operate the microscope at AFF condition effectively, highly stabilized electron beams with small energy spread and small beam divergence are necessary. In the present observation, a 120 kV electron microscope with LaB6 electron gun was used. The most of the images were taken with the direct electron optical magnification of 1.3 million times and then magnified photographically.1. Twist boundary of ZnSFig. 1 is the image of wurtzite single crystal with twist boundary grown on the surface of zinc crystal by the reaction of sulphur vapour of 1540 Torr at 500°C. Crystal surface is parallel to (00.1) plane and electron beam is incident along the axis normal to the crystal surface. In the twist boundary there is a dislocation net work between two perfect crystals with a certain rotation angle.

Observation of secondary slip systems in tungsten bicrystals

1984 ◽  
Vol 42 ◽  
pp. 478-479
Author(s):  
J. R. Fekete ◽  
R. Gibala
Keyword(s):  
Stress Field ◽  
Grain Boundaries ◽  
Deformation Behavior ◽  
Stress Axis ◽  
Polycrystalline Materials ◽  
Slip Systems ◽  
Metallic Materials ◽  
Twist Boundary ◽  
Secondary Slip ◽  
Plane Normal

The deformation behavior of metallic materials is modified by the presence of grain boundaries. When polycrystalline materials are deformed, additional stresses over and above those externally imposed on the material are induced. These stresses result from the constraint of the grain boundaries on the deformation of incompatible grains. This incompatibility can be elastic or plastic in nature. One of the mechanisms by which these stresses can be relieved is the activation of secondary slip systems. Secondary slip systems have been shown to relieve elastic and plastic compatibility stresses. The deformation of tungsten bicrystals is interesting, due to the elastic isotropy of the material, which implies that the entire compatibility stress field will exist due to plastic incompatibility. The work described here shows TEM observations of the activation of secondary slip in tungsten bicrystals with a [110] twist boundary oriented with the plane normal parallel to the stress axis.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional
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