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Acta Physica Polonica A

Doped Carrier Formulation of the t-J model: Monte Carlo Study of the Anisotropic Case

A. Ferraz, E. A. Kochetov, Maciej M. Maśka, Marcin Mierzejewski

Published Jul 1, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.114.185

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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.
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.
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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.
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-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.
The extended Hubbard model with nearest neighbour inter-site correlations has been studied by mapping it onto a spin-Hamiltonian. In the case of a half-filled band the problem is equivalent to that of an anisotropic Heisenberg model in the absence of a field. The phases in the U-Q plane obtained here are in good agreement with those obtained by Monte Carlo simulation. The antiferromagnetic XY-ordered phase of the model is shown to be very similar to an RVB phase. Extending the analogy away from half-filling, a possible dependence of the critical temperature T c with the doping concentration delta in a high-T c system is suggested.
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.