Non-local spacetime supersymmetry on the lattice
Non-local spacetime supersymmetry on the lattice
复制标题
晶格上的非局域时空超对称性
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
P. Fendley
中科院分区：
文献类型：
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作者：
X. Yang;P. Fendley
我们证明了几个著名的一维量子系统具有隐藏的非局域超对称性。最简单的例子是开放的 XXZ 自旋链，其中 Δ = −1/2。我们利用超对称性为具有各种边界条件的基态能量设置下限。对于周期链中的奇数个位点，并且在开链中具有特定的边界磁场，我们可以准确地推导出基态能量。因此，超对称性解释了为什么在这些情况下可以求解基态的贝特方程。我们还表明，类似的时空超对称性对于 t-J 模型在其可积铁磁点也成立，其中时空超对称性及其产生的哈密顿量与全局 u(1|2) 分级李代数对称性共存。讨论了对其他代数的可能推广。
We show that several well-known one-dimensional quantum systems possess a hidden non-local supersymmetry. The simplest example is the open XXZ spin chain with Δ = −1/2. We use the supersymmetry to place lower bounds on the ground-state energy with various boundary conditions. For an odd number of sites in the periodic chain, and with a particular boundary magnetic field in the open chain, we can derive the ground-state energy exactly. The supersymmetry thus explains why it is possible to solve the Bethe equations for the ground state in these cases. We also show that a similar spacetime supersymmetry holds for the t–J model at its integrable ferromagnetic point, where the spacetime supersymmetry and the Hamiltonian it yields coexist with a global u(1|2) graded Lie algebra symmetry. Possible generalizations to other algebras are discussed.