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arXiv:cond-mat/9809362 · Physical review. B, Condensed matter

Mean-field description of the phase string effect in the t−J model

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

Published Apr 1, 1999• 43 citations
arXivHTMLPDF

Abstract

A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.

DOI
10.1103/physrevb.59.8943

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A mean-field treatment of the phase string effect in the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.
Magnetic Order and Superconductivity in the Bosonic t-J Model of CP1^11 Spinons and Doped Bosonic Holons
We study the three-dimensional U(1) lattice gauge theory of a CP1^11 spinon (Schwinger boson) field and a Higgs field. It is a bosonic ttt-JJJ model in slave-particle representation, describing the antiferromagnetic (AF) Heisenberg spin model with doped bosonic holes expressed by the Higgs field. The spinon coupling term of the action favors AF long-range order, whereas the holon hopping term in the ferromagnetic channel favors Bose-Einstein condensation (BEC) of holons. We investigate the phase structure by means of Monte-Carlo simulations and study an interplay of AF order and BEC of holes. We consider the two variations of the model; (i) the three-dimensional model at finite temperatures, and (ii) the two-dimensional model at vanishing temperature. In the model (i) we find that the AF order and BEC coexist at low temperatures and certain hole concentrations. In the model (ii), by varying the hole concentration and the stiffness of AF spin coupling, we find a phase diagram similar to the model (i). Implications of the results to systems of cold atoms and the fermionic ttt-JJJ model of strongly-correlated electrons are discussed.
We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped Mott insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the $t\text{\ensuremath{-}}J$ model. We show that the well-known spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. These properties are consistent with experimental observations in the high-Tc{T}_{c}Tc​ cuprates. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.
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