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arXiv:0901.0878 · AIP conference proceedings

Polaron in the t-J Models with Three-site Terms: the SU(2) and the Ising Cases

Krzysztof Wohlfeld, Adolfo Avella, Ferdinando Mancini

Published Jan 1, 2008• 0 citations
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Abstract

We compare the role of the three‐site terms added to the t‐J models in the SU(2) and the Ising cases in the extremely low doping regime, i.e. when a single hole added to the strongly interacting half‐filled system becomes a polaron. We show that in the realistic Ising case the three‐site terms play a vital role in the polaron movement and should never be neglected unlike in the SU(2) case.

DOI
10.1063/1.2940444

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We compare the role of the three‐site terms added to the t‐J models in the SU(2) and the Ising cases in the extremely low doping regime, i.e. when a single hole added to the strongly interacting half‐filled system becomes a polaron. We show that in the realistic Ising case the three‐site terms play a vital role in the polaron movement and should never be neglected unlike in the SU(2) case.
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.
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.
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.
The $t\ensuremath{-}J$ model is a standard model of strongly correlated electrons, often studied in the context of high-Tc{T}_{c}Tc​ superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange JJJ. As these terms correspond to pair hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half filling. We present a density matrix renormalization-group study of the one-dimensional $t\ensuremath{-}J$ model with the pair hopping terms included. We demonstrate that these additional terms radically change the one-dimensional ground-state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.
We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO2{}_{2}2​ layer. The low-energy wave functions for two doped holes introduced in a half filled CuO2{}_{2}2​ plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ states. Last, we point out features that are expected to be robust for larger systems.