Ground state representation of the infinite one‐dimensional Heisenberg ferromagnet. III. Scattering theory

1978 ◽  
Vol 19 (8) ◽  
pp. 1699-1704 ◽  
Author(s):  
Donald Babbitt ◽  
Lawrence Thomas
Keyword(s):  
Ground State ◽  
Scattering Theory ◽  
Heisenberg Ferromagnet ◽  
State Representation ◽  
One Dimensional

Effect of Biquadratic Exchange on Two Magnon States of Heisenberg Ferromagnets: Other Neighbor Exchange

1975 ◽  
Vol 53 (6) ◽  
pp. 637-647 ◽  
Author(s):  
D. A. Pink ◽  
Vijay Sachdeva
Keyword(s):  
Ground State ◽  
Nearest Neighbor ◽  
Ferromagnetic State ◽  
Localized States ◽  
Heisenberg Ferromagnet ◽  
Green Functions ◽  
Localized Modes ◽  
One Dimensional ◽  
Localized State ◽  
Biquadratic Exchange

We have investigated the two magnon localized states of a one dimensional Heisenberg ferromagnet the Hamiltonian of which is made up of nearest neighbor and next nearest neighbor isotropic bilinear and biquadratic exchange terms, and a single ion anisotropy term. We have restricted our choice of parameters so that the ground state at T = 0 is the fully aligned ferromagnetic state and we have used the thermodynamic Green functions where the averages have been evaluated in the ground state so that our results are good for [Formula: see text]. We have evaluated the probabilities of finding two spin deviations a distance n apart when the system is in a localized state described by total wave vector q. We have (a) compared the effects of ferromagnetic and antiferromagnetic next nearest neighbor exchange, (b) found that localized modes can lie below or above the two free magnon band depending upon the sign and magnitude of the biquadratic exchange, (c) found that in certain cases two spin deviations appear to behave like objects interacting only via a soft core, and (d) found that modes can have a large single ion component when the single ion anisotropy is zero.

scholarly journals Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Przemysław Kościk ◽  
Arkadiusz Kuroś ◽  
Adam Pieprzycki ◽  
Tomasz Sowiński
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Pair Correlation ◽  
Contact Interactions ◽  
One Dimensional ◽  
Particle Correlations ◽  
Variational Scheme ◽  
Full Control ◽  
Arbitrary Shapes

AbstractWe derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

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