论文标题
如何使用Lie代数定义量子平均可溶解的哈密顿量
How to define quantum mean-field solvable Hamiltonians using Lie algebras
论文作者
论文摘要
到目前为止，尚未制定量子哈密顿量在平均场理论中可以完全解决的必要条件。为了解决这个问题，首先，我们定义了什么是含义场理论是什么，而不是在特定的一组运营商中实现的哈密顿式实现。其次，使用谎言代数框架，我们制定了一个标准，使哈密顿量可以溶解。该标准适用于可区分和无法区分的粒子案例。对于电子哈密顿人来说，我们的方法揭示了比二次官能运营商更高的菲尔米式操作员力量的平均野外可解决的哈密顿量。一些平均可溶解的汉密尔顿人需要不同的本征态的不同类粒子旋转，这反映了这种哈密顿量的更为复杂的结构。
Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field theories have not been formulated so far. To resolve this problem, first, we define what mean-field theory is, independently of a Hamiltonian realization in a particular set of operators. Second, using a Lie-algebraic framework we formulate a criterion for a Hamiltonian to be mean-field solvable. The criterion is applicable for both distinguishable and indistinguishable particle cases. For the electronic Hamiltonians, our approach reveals the existence of mean-field solvable Hamiltonians of higher fermionic operator powers than quadratic. Some of the mean-field solvable Hamiltonians require different sets of quasi-particle rotations for different eigenstates, which reflects a more complicated structure of such Hamiltonians.
