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arXiv:1507.00774 · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

The Ising version of thet–Jmodel

Maciej M. Maśka, Marcin Mierzejewski, Evgeny Kochetov

Published Nov 5, 2014• 8 citations
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Abstract

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.

DOI
10.1080/14786435.2014.977371

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Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.

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We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-${\mathit{T}}_{\mathit{c}}$ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.

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Effect of Exclusion of Double Occupancies in t-J Model: Extension of Gutzwiller Approximation

Masao Ogata, Akihiro Himeda

A new type of analytic estimation of the effect of strong correlation is developed for the two-dimensional t-J model. It is based on the Gutzwiller approximation which gives the renormalization of parameters, t and J, due to the Gutzwiller's projection operator excluding the double occupancies. The finite-range correlations are taken into account compared with the conventional Gutzwiller approximation where only the on-site expectation values are considered. It is shown that the essential point of the renormalization is its nonlinear dependence on the expectation values of Cooper pairs and antiferromagnetic moment. In particular the renormalization factor of J becomes anisotropic in the presence of antiferromagnetic moment, i.e., that for the z-component is enhanced compared with that for the xy-component. The physical origin of this enhancement is identified as the surrounding antiferromagnetic correlations of a bond. The self-consistency equations for the uniform variational wave functions are derived and solved numerically. Our result gives a reasonable estimate of antiferromagnetic order parameters near half filling, in contrast to the conventional slave-boson mean-field theory and the original Gutzwiller approximation. It is also found that, at half filling, the renormalization of J represents some of the quantum fluctuations of the Heisenberg spin system in a different manner from the spin-wave theory. For finite doping, our results have some similarity to SO(5) symmetric theory. Applications to the inhomogeneous systems such as the vortex state, around nonmagnetic impurities, and stripe state are discussed.

arXiv:cond-mat/0003465•Mar 29, 2000•0 citations
The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.
Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.
Abstract. Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t–J model. This model possesses the global discrete Z2 symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t–J model, usually referred to as the t–Jz model, the global SU(2) invariance is fully restored at Jz = 0, so that only the spin-spin interaction has in that model the true Ising form. We discuss a relationship between those two models and the standard isotropic t–J model. We show that the low-energy quasiparticles in all three models share the qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t–J model over the t–Jz one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10 3 sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next nearest neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no double occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed. PACS numbers: 71.10.Fd, 71.10.Pm, 74.25.JbIsing t–J model close to half filling: A Monte Carlo study 2 1.
We discuss the relevance of the improved mean-field slave-fermion theory to describe the Nagaoka $(U=\ensuremath{\infty})$ limit of the Hubbard model. In this theory the crucial on-site constraint of no double electron occupancy is taken into account rigorously prior to the mean-field approximation. At one-loop approximation the effective mean-field action shows a long-range ferromagnetic order over the whole doping range. This indicates that the slave-fermion mean-field theory does not constitute an appropriate framework to describe the physics of the Nagaoka phase. We discuss the drawbacks of this mean-field theory and present some results on the derivation of a low-energy effective spin action to describe the Nagaoka phase beyond the mean-field approximation.
We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.
A new type of analytic estimation of the effect of strong correlation is developed for the two-dimensional t-J model. It is based on the Gutzwiller approximation which gives the renormalization of parameters, t and J, due to the Gutzwiller's projection operator excluding the double occupancies. The finite-range correlations are taken into account compared with the conventional Gutzwiller approximation where only the on-site expectation values are considered. It is shown that the essential point of the renormalization is its nonlinear dependence on the expectation values of Cooper pairs and antiferromagnetic moment. In particular the renormalization factor of J becomes anisotropic in the presence of antiferromagnetic moment, i.e., that for the z-component is enhanced compared with that for the xy-component. The physical origin of this enhancement is identified as the surrounding antiferromagnetic correlations of a bond. The self-consistency equations for the uniform variational wave functions are derived and solved numerically. Our result gives a reasonable estimate of antiferromagnetic order parameters near half filling, in contrast to the conventional slave-boson mean-field theory and the original Gutzwiller approximation. It is also found that, at half filling, the renormalization of J represents some of the quantum fluctuations of the Heisenberg spin system in a different manner from the spin-wave theory. For finite doping, our results have some similarity to SO(5) symmetric theory. Applications to the inhomogeneous systems such as the vortex state, around nonmagnetic impurities, and stripe state are discussed.