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arXiv:cond-mat/0611774 · Physical Review B

Antiferromagnetism in two-dimensional t−J model: A pseudospin representation

Daisuke Yamamoto, Susumu Kurihara

Published Apr 30, 2007• 6 citations
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Abstract

We discuss a pseudospin representation of the two-dimensional $t\text{\ensuremath{-}}J$ model. We introduce pseudospins associated with empty sites, deriving a representation of the $t\text{\ensuremath{-}}J$ model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of $t\text{\ensuremath{-}}J$ model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping $\ensuremath{\delta}$ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green's function method, we show that the staggered magnetization decreases with increasing hole doping $\ensuremath{\delta}$ and disappears at $\ensuremath{\delta}\ensuremath{\approx}0.06--0.12$ for $t∕J=2.5--5$. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.

DOI
10.1103/physrevb.75.134520

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We discuss a pseudospin representation of the two-dimensional t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. We introduce pseudospins associated with empty sites, deriving a representation of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping \ensuremathδ\ensuremath{\delta}\ensuremathδ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green's function method, we show that the staggered magnetization decreases with increasing hole doping \ensuremathδ\ensuremath{\delta}\ensuremathδ and disappears at \ensuremathδ\ensuremath≈0.06−−0.12\ensuremath{\delta}\ensuremath{\approx}0.06--0.12\ensuremathδ\ensuremath≈0.06−−0.12 for t∕J=2.5−−5t∕J=2.5--5t∕J=2.5−−5. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.
This report discusses the slave-fermion representations of the $t\ensuremath{-}J$ model and describes another representation in which fermions and bosons are completely commuting. For a study of the system in the new representation at half-filling, the interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.
The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the properties of physical holes. For a study of the system in the new representation at half-filling, interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
Local magnetic moments induced by a nonmagnetic impurity in the two-dimensional $t\ensuremath{-}J$ model are investigated by use of a Green function method in a finite-size system (50\ifmmode\times\else\texttimes\fi{}50=2500 sites). Local electron number and nearest-neighbor correlation functions are calculated self-consistently at each lattice point. A local electron number distribution shows that electrons form a bound state around an impurity site and the magnitude of the local moment is enhanced, whereas doped holes can be distributed only apart from the impurity site and destroy an antiferromagnetic spin configuration by their motion. This result is consistent with experimental results of Zn-doped high-Tc{T}_{c}Tc​ superconductors.
The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the properties of physical holes. For a study of the system in the new representation at half-filling, interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models working within the limits of spin-wave theory by linearizing the hole-spin-deviation interaction and by adapting the noncrossing approximation. We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both $t\ensuremath{-}J$ and $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ models. Furthermore, our results show that the residue of the quasiparticle peak at $\stackrel{P\vec}{G}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ decreases very rapidly with doping. We also find pockets centered at $\stackrel{P\vec}{G}$, (i) with an elliptical shape with large eccentricity along the antinodal direction in the case of the $t\ensuremath{-}J$ model and (ii) with an almost circular shape in the case of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model. Last, we show that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like pattern along the nodal direction of the Brillouin zone, a feature that is also seen in angle-resolved photoemission spectroscopy measurements.