Solving local constraint conditions in slave particle theory

Abstract

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 ${\lambda }_i$ which ensures the constraint: In the Hamiltonian formalism of the theory, ${\lambda }_i$ is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism, ${\lambda }_i(t)$ becomes time-dependent and plays a role of gauge field. This implies that the redundant degrees of freedom of ${\lambda }_i(t)$ are introduced and must be removed by the additional constraint, the gauge fixing condition ${\partial }_t{\lambda }_i(t)=0$. 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 ${\lambda }_i(t)$ 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 ${\lambda }_i(t)$ 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.

arXiv comment9 pages, revised version, Commun. Theor. Phys. in press

References in corpus (12)

• A Common Thread: the pairing interaction for the unconventional superconductors
• Theory of Underdoped Cuprates
• The Physics Behind High-Temperature Superconducting Cuprates: The "Plain Vanilla" Version Of RVB
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems
• The mechanism of spin and charge separation in one dimensional quantum antiferromagnets
• Renormalized mean-field t-J model of high-Tc superconductivity: comparison with experiment
• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Coexistence of $s$- and $d$-wave gaps due to pair-hopping and exchange interactions
• Understanding high-Tc cuprates based on the phase string theory of doped antiferromagnet
• Gauge theory of the Hubbard model on honeycomb lattice and its instanton effect

Cited by in corpus (1)

• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints