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Physical review. B, Condensed matter

Comment on “BCS-type mean-field theory for the t−J model in the SU(2|1) superalgebra representation”

Nikolay M. Plakida, V. Yu. Yushankhaï

Published Jul 7, 2003• 0 citations
Publisher

Abstract

We show that the phase diagram and the odd p-wave quasiparticle gap for spinless fermions obtained in the paper by Kochetov and Mierzejewski for the $t\ensuremath{-}J$ model are artifacts of the adopted spin-charge separation treated in mean field approximation, while the critical remarks concerning the theory of exchange superconducting pairing derived within the Hubbard operator approach are misleading.

DOI
10.1103/physrevb.68.016501

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BCS-type mean-field theory for the t−J model in the SU(2|1) superalgebra representation

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Reply to “Comment on ‘BCS-type mean-field theory for the t−J model in the SU(2|1) superalgebra representation’ ”

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We show that the $\mathrm{SU}(2|1)$-superalgebra path-integral representation for the partition function of the $t\ensuremath{-}J$ model follows from the conventional slave-fermion path-integral representation under a change of variables that explicitly resolves the constraint of no double occupancy.

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We show that the phase diagram and the odd p-wave quasiparticle gap for spinless fermions obtained in the paper by Kochetov and Mierzejewski for the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model are artifacts of the adopted spin-charge separation treated in mean field approximation, while the critical remarks concerning the theory of exchange superconducting pairing derived within the Hubbard operator approach are misleading.
A simple version of the Bardeen-Cooper-Schrieffer (BCS)-type mean-field theory for the $t\ensuremath{-}J$ model is developed. The present approach rigorously treats the constraint of no doubly occupied states and invokes two local order parameters to implement spontaneous breaking of the global $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry. This is achieved by identifying the Hubbard operators with generators of the SU(2∣1)\mathrm{SU}(2|1)SU(2∣1) superalgebra in the fundamental representation and employing the ensuing CP1∣1{\mathrm{CP}}^{1|1}CP1∣1 parametrization for dynamical variables. As a result, an improved phase diagram ${T}_{c}(\ensuremath{\delta})$ in the paramagnetic phase is obtained.
We show that the SU(2∣1)\mathrm{SU}(2|1)SU(2∣1)-superalgebra path-integral representation for the partition function of the $t\ensuremath{-}J$ model follows from the conventional slave-fermion path-integral representation under a change of variables that explicitly resolves the constraint of no double occupancy.
We show that the $t\ensuremath{-}J$ Hamiltonian is not in general reduced to ${H}_{t\ensuremath{-}J}=H(S\ensuremath{\rightarrow},f)$, where $S\ensuremath{\rightarrow}$ and fff stand for independent $([S\ensuremath{\rightarrow},f]=0)$ SU(2) (spin) generators and spinless fermionic (holon) fields, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su(2∣1)(2|1)(2∣1) superalgebra in the degenerate fundamental representation and ensuing SU(2∣1)(2|1)(2∣1) path-integral representation of the partition function ${Z}_{t\ensuremath{-}J}.$
The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.
The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through ladder-type diagrams in the particle-hole channel. The resulting phase diagram for the (quasi-)two-dimensional Hubbard model exhibits antiferromagnetism and ddd-wave superconductivity. Furthermore, a uniform charge instability, i.e., phase separation, is obtained in the low-doping regime around the Mott insulator. We also examine spin/charge density wave fluctuations including ddd-wave symmetry. The model exhibits a tendency towards an unconventional charge density wave, but no divergence of the susceptibility is found.