Unitary flow of the bosonized large-N Lipkin model
Unitary flow of the bosonized large-N Lipkin model
复制标题
玻色大 N Lipkin 模型的酉流
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
J. Stein
中科院分区：
文献类型：
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作者：
J. Stein
对于Holstein-Primakoff玻色子表象中的Lipkin模型和大粒子数N，导出了描述连续幺正变换的流方程，并精确求解了该变换使哈密顿量更接近对角性.变换后的哈密顿量是1/N 3阶对角的，将已知的线性变换扩展到下一个更高阶的逆粒子数。这种方法很自然地允许人们在变换过程中保持原利普金哈密顿量的三对角结构。给出了耦合函数的精确解析结果，给出了基态能量和第一激发态能隙的1/N2级显式表达式，并与精确数值进行了比较.
The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N . The transformed Hamiltonian is diagonal in order 1/N 3 , extending known linear transformations to next-higher orders in the inverse particle number. This approach quite naturally allows one to preserve the tridiagonal structure of the original Lipkin Hamiltonian in the course of the transformation. Exact analytical results for the coupling functions and explicit expressions for the ground state energy and for the energy gap to the first excited state in order 1/N 2 are presented and are compared with the accurate numerical values.