On the Validity of Hidden Fermi Liquid Theory

Abstract

Philip Anderson's hidden Fermi liquid theory is a promising candidate for the definitive theory of the "strange metal" phase of the cuprates. We here investigate some of the outstanding issues with the hidden Fermi liquid theory to see whether this is indeed a consistent and correct theory of the strange metal. After outlining the theory, we first investigate the validity of the Gutzwiller approximation, a mathematical tool upon which the hidden Fermi liquid theory heavily relies. We determine the conditions under which this approximation can be used, and we identify and correct a common error made in the literature about the Gutzwiller factor for the J term of the t-J Hamiltonian. We also discuss the relationship between the Gutzwiller approximation and the technique of renormalized mean field theory. We then seek to put the derivation of the Green's function for our system on more rigorous footing than the outline provided by Anderson. We confirm the factorization of the Green's function into a noninteracting component and a projective correction, and we confirm that these evolve in time according to a noninteracting effective Hamiltonian. Anderson's fugacity factors follow naturally from this new derivation, whereas earlier work inserted these factors in an ad hoc fashion. However, we find a flaw in the original derivation of the projective correction. We calculate the correct expression for this quantity and discuss the implications for hidden Fermi liquid theory, finding that the theory should be able to incorporate this change with only slight modifications.