论文标题
解决从奴隶粒子理论中解决局部约束条件
Solving local constraint conditions in slave particle theory
论文作者
论文摘要
通过对仪表理论的Becchi-Rouet-stora-tyutin（BRST）量化，我们解决了局部约束条件的长期困难问题，即每个位置的单位粒子的单个占用，在从属粒子理论中。这种困难实际上是由于不一致的处理本地Lagrange乘数$λ_i$引起的，这确保了限制：在理论上的汉密尔顿形式主义中，$λ_i$是与时间无关的，并且与汉密尔顿人通勤，而在Lagrangian形式上，在Lagrangian形式上，$λ_i（t）$ with lige依赖于时间依赖于时间依赖于时间依赖于时间的领域。这意味着引入了$λ_i（t）$的冗余自由度，必须通过附加约束来删除量规固定条件$ \partial_tλ_i（t）= 0 $。在文献中，错过了这种量规固定条件。我们添加了这种规格的固定条件，并将量规理论的BRST量化用于从从属粒子理论中的Dirac的一流约束。该规格固定条件赋予$λ_i（t）$具有动力学，并带来重要的物理结果。例如，我们在半填充时研究了哈伯德模型，并发现Spinon夹在弱$ U $中，并且该系统确实是一种常规金属，它可以解决悖论，即弱耦合状态是先前的奴隶玻色子平均场理论中的超导体。对于$ t $ - $ j $型号，我们发现$λ_i（t）$的动态效应实质上抑制了$ d $ - 波配对差距，然后将超导临界温度降低至少降低平均野外值的五分之一，这是1000 k的顺序。
With the Becchi-Rouet-Stora-Tyutin (BRST) quantization of gauge theory, we solve the long-standing difficult problem of the local constraint conditions, i.e., the single occupation of a slave particle per site, in the slave particle theory. This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier $λ_i$ which ensures the constraint: In the Hamiltonian formalism of the theory, $λ_i$ is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism, $λ_i(t)$ becomes time-dependent and plays a role of gauge field. This implies that the redundant degrees of freedom of $λ_i(t)$ are introduced and must be removed by the additional constraint, the gauge fixing condition $\partial_t λ_i(t)=0$. In literature, this gauge fixing condition was missed. We add this gauge fixing condition and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory. This gauge fixing condition endows $λ_i(t)$ with dynamics and leads to important physical results. As an example, we study the Hubbard model at half-filling and find that the spinon is gapped in the weak $U$ and the system is indeed a conventional metal, which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field theory. For the $t$-$J$ model, we find that the dynamic effect of $λ_i(t)$ substantially suppresses the $d$-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the mean field value which is of the order of 1000 K. The renormalized $T_c$ is then close to that in cuprates.
