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arXiv:0705.2937 · Physical Review B

Doped carrier formulation of the t−J model: Projection constraint and the effective Kondo-Heisenberg lattice representation

Rafael Tristão Pepino, Álvaro Antônio Bandeira Ferraz, Evgueny Kochetov

Published Jan 24, 2008• 15 citations
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Abstract

We show that the recently proposed doped carrier Hamiltonian formulation of the $t\text{\ensuremath{-}}J$ model should be complemented with the constraint that projects out the unphysical states. With this important ingredient, the previously used and seemingly different spin-fermion representations of the $t\text{\ensuremath{-}}J$ model are shown to be gauge related to each other. This constraint can be treated in a controlled way close to half-filling, suggesting that the doped carrier representation provides an appropriate theoretical framework to address the $t\text{\ensuremath{-}}J$ model in this region. This constraint also suggests that the $t\text{\ensuremath{-}}J$ model can be mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights important physical similarities between the quasi-two-dimensional heavy fermions and the high-${T}_{c}$ superconductors. Finally, we discuss the physical implications of our model representation relating, in particular, the small versus large Fermi surface crossover to the closure of the lattice spin gap.

DOI
10.1103/physrevb.77.035130

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We show that the recently proposed doped carrier Hamiltonian formulation of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model should be complemented with the constraint that projects out the unphysical states. With this important ingredient, the previously used and seemingly different spin-fermion representations of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model are shown to be gauge related to each other. This constraint can be treated in a controlled way close to half-filling, suggesting that the doped carrier representation provides an appropriate theoretical framework to address the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model in this region. This constraint also suggests that the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model can be mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights important physical similarities between the quasi-two-dimensional heavy fermions and the high-Tc{T}_{c}Tc​ superconductors. Finally, we discuss the physical implications of our model representation relating, in particular, the small versus large Fermi surface crossover to the closure of the lattice spin gap.
We derive a doped carrier representation of the t-J model Hamiltonian.Within this approach the t-J model is described in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator.This representation of the t-J Hamiltonian is very convenient for underdoped systems since close to half-filling it allows for a controlled treatment of the crucial constraint of no doubly occupied sites.When neglecting the transverse spin-spin interaction, the effective Hamiltonian can be investigated with classical Monte Carlo simulations.We discuss the results obtained for systems consisting of several hundred lattice sites.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
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.
In the generalized-tJtJtJ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-tJtJtJ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and ddd-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.
We study one dimensional {\it extended} Kondo lattice model, described by the t−Jt-Jt−J Hamiltonian for conduction electrons away from half filling and the Heisenberg Hamiltonian for localized spins at half filling. Following Shankar,\cite{Shankar} we find an effective field theory for this model, where doped holes are represented by massless Dirac fermions (holons) and spin excitations are fractionalized into relativistic bosons (spinons). These holons and spinons interact via U(1) gauge fluctuations. Effects of Berry phase to the localized spins disappear due to the presence of Kondo couplings, causing the spinon excitations gapped. Furthermore, the gauge fluctuations are suppressed by hole doping. As a result, massive spinons are deconfined to arise in the localized spins unless the Kondo hybridization is strong enough. When the Kondo hybridization strength exceeds a certain value, we find that the localized spin chain becomes critical. This indicates that the present one dimensional Kondo lattice model exhibits a phase transition from a spin-gapped phase to a critical state in the localized spin chain, driven by the Kondo interaction.