Magnon–phonon interaction in the one dimensional quantum XY model

2004 ◽  
Vol 129 (10) ◽  
pp. 621-626 ◽  
Author(s):  
A.S.T. Pires
Keyword(s):  
Xy Model ◽  
Phonon Interaction ◽  
One Dimensional ◽  
The One

scholarly journals Out-of-time-order correlators in the one-dimensional XY model

2020 ◽  
Vol 72 (8) ◽  
pp. 085103
Author(s):  
Jia-Hui Bao ◽  
Cheng-Yong Zhang
Keyword(s):  
Xy Model ◽  
One Dimensional ◽  
Time Order ◽  
The One

scholarly journals Markovian and Non-Markovian Dynamics in the One-Dimensional Transverse-Field XY Model

2019 ◽  
Vol 176 (2) ◽  
pp. 492-504
Author(s):  
Z. Saghafi ◽  
S. Mahdavifar ◽  
E. Hosseini Lapasar
Keyword(s):  
Transverse Field ◽  
Xy Model ◽  
One Dimensional ◽  
Markovian Dynamics ◽  
The One

scholarly journals Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

2018 ◽  
Vol 3 (4) ◽  
pp. 32
Author(s):  
Shiung Fan
Keyword(s):  
Ground State ◽  
Spin Chains ◽  
Xy Model ◽  
One Dimensional ◽  
Wigner Transformation ◽  
Lattice Fermions ◽  
Large Systems ◽  
The One ◽  
Periodic Chain ◽  
Non Locality

The Jordan–Wigner transformation plays an important role in spin models. However, the non-locality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N − 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an anti-periodic chain of lattice fermions without redundancy when the Jordan–Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model ( σ x σ y − σ x σ y ) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites.

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