Solving local constraint condition problem in slave particle theory with the BRST quantization  

作　　者：Xi Luo Jianqiao Liu Yue Yu 

机构地区：[1]College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China [2]Department of Physics,Fudan University,Shanghai 200433,China

出　　处：《Communications in Theoretical Physics》2023年第9期173-181,共9页理论物理通讯(英文版)

基　　金：supported by NNSF of China with No. 12174067。

摘　　要：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(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC 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(MF) 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 MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.

关 键 词：slave particle BRST gauge theory high T_c superconductivity Hubbard model t–J model 

分 类 号：O469[理学—凝聚态物理]