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arXiv:0810.4643 · Journal of Physics Condensed Matter

Isingt–Jmodel close to half filling: a Monte Carlo study

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

Published Jan 8, 2009• 5 citations
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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 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.

DOI
10.1088/0953-8984/21/4/045703

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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.
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 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–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.
A next-nearest-neighbor hopping t' in the t-t'-J model has a different sign between the hole- and electron-doped systems of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates: t'0 for the hole-doped system and t'>0 for the electron-doped system. We show that the sign is responsible for the remarkable difference of antiferromagnetic (AF) phases between the two systems. To reveal this and clarify the role of t', we examine magnetic excitations of the t-t'-J model by employing exact diagonalization techniques for 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattices. In the low-doping region (two-hole case of the \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattice), AF spin correlations are stabilized for the case of t'>0, i.e., electron-doping case, but not for the case of t'0. In the high-doping region (four-hole case of the 4\ifmmode\times\else\texttimes\fi{}4 lattice and more) magnetic excitations are mainly controlled by the geometry of the Fermi surface of the noninteracting system.
Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.
We map out the ground-state phase diagram of a one-dimensional SU(N)\mathrm{SU}(N)SU(N) Kondo-Heisenberg lattice model at half-filling and in the fully antisymmetric self-adjoint representation as a function of 1N\frac{1}{N}N1​ and Kondo coupling Jk/t{J}_{k}/tJk​/t. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even NNN up to 8, we show that the enlarged $\mathrm{SU}(N\ensuremath{\ge}4$) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak-coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong Jk/t{J}_{k}/tJk​/t limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing Jk/t{J}_{k}/tJk​/t, we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized fff spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-NNN approximation, and we show that in the limit of infinite degeneracy $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized fff spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling Jh=0{J}_{h}=0Jh​=0, and we provide evidence that the enlarged SU(N)\mathrm{SU}(N)SU(N) symmetry and low dimensionality of the Ruderman-Kittel-Kasuya-Yosida exchange interaction are not sufficient to induce VBS order in the conventional SU(N)\mathrm{SU}(N)SU(N) Kondo chain, which hosts solely a KI phase. Finally, we quantify the role of increasing NNN in reducing the separation of charge and spin timescales specific to the KI state, and we show that the latter is adiabatically connected to a trivial band insulator captured by the large-NNN approximation.