A Detailed Numerical Analysis for High-Tc Superconductivity and Physical Analysis of the High-Tc Phase Diagram Based on the U(1) Slave-Boson Approach to the t − J Hamiltonian

Abstract

One of the major theoretical challenges in high-Tc superconductivity is to first reproduce the observed phase diagrams that display the monotonously decreasing pseudogap temperature T* and the dome-shaped superconducting phase transition temperature Tc in the plane of temperature vs. hole concentration. Earlier Lee and Salk [J. Korean Phys. Soc. 37, 545 (2000); Phys. Rev. B 64, 052501 (2001)] reported a successful reproduction of the phase diagram by providing a realistic gauge theoretic [SU(2)/U(1)] slave-boson approach to the t - J Hamiltonian. Most recently, we [S.-H. S. Salk, Quantum Studies: Mathematics and Foundations 5, 149 (2018)] presented a comprehensive discussion on both the SU(2) and the U(1) approaches from which one can readily understand the intimate relationship between the two formalisms and discussed that both approaches can lead to room-temperature superconductivity with suitably high values of the antiferromagnetic coupling constant J, owing to the demonstration of identical physical propensities, i.e., the higher the J is, the higher the superconducting phase transition temperature Tc is. Here, we discuss hither-to-unreported detailed numerical computations of the phase diagrams by varying the values of J by using the U(1) gauge slave-boson approach to the t − J Hamiltonian. For the sake of testing convergence, we vary the unit-cell lattice sizes from 10 × 10 to a sufficiently large size of 50 × 50. We find that even a small square lattice size of 20 × 20 is seen to show reliable agreement with the results for higher lattice sizes while the 50 × 50 lattice size displays complete convergence in both T*and Tc. In addition, we present a physical analysis of the structure of the high-Tc phase diagram, focusing on the role of the spin pairing order in association with the interplay between the pseudo-gap (spin gap) temperature and the bose-condensation temperature/dome-shaped superconducting phase transition temperature.