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Physical review. B, Condensed matter

Interaction between two spin polarons in one- and two-dimensional quantum-spin systems

Kunio Ishida, Hiroshi Kamimura

Published Nov 1, 1990• 4 citations
Publisher

Abstract

One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high-${\mathit{T}}_{\mathit{c}}$ superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ``doped'' Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.

DOI
10.1103/physrevb.42.8312

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One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ``doped'' Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.
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.
The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.
The stability of the spin polaron quasiparticle, well established in studies of a single hole in the 2D antiferromagnets, is investigated in the 1D antiferromagnets using a t t - J J model. We perform an exact slave fermion transformation to the holon-magnon basis, and diagonalize numerically the resulting model in the presence of a single hole. We demonstrate that the spin polaron collapses - and the spin-charge separation takes over - due to the specific role played by the magnon-magnon interactions and the magnon hard-core constraint in the 1D t t - J J model. Moreover, we prove that the spin polaron is stable for any strength of the magnon-magnon interaction other than the unique value found in a 1D antiferromagnet with the continuous symmetry of the spin interactions. Fine-tuning to this unique value is extremely unlikely to occur in quasi-1D antiferromagnets, therefore the spin polaron is the stable quasiparticle of realistic 1D materials. Our results lead to a new interpretation of the ARPES spectra of quasi-1D antiferromagnets in the spin polaron language.
Even though realistic one-dimensional experiments in the field of half-metallic semiconductors are not at hand yet, we are interested in the underlying fundamental physics. In this regard we study a one-dimensional ferromagnetic Kondo lattice model, a model in which a conduction band is coupled ferromagnetically to a background of localized d moments with coupling constant J(H), and investigate the T = 0 phase diagram as a function of the antiferromagnetic interaction J between the localized moments and the band-filling n, since it has been observed that doping of the compounds has led to formation of magnetic domains. We explore the spin-polaron formation by looking at the nearest-neighbour correlation functions in the spin and charge regimes for which we use the density matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.
The understanding of matter does not only require a precise analysis of individual characteristics of the fundamental constituents, but also the study of their collective behavior.Solid state physics, and in particular research in strongly correlated electron systems, deals with such collective phenomena.The properties of the electrons, charge and spin quantum numbers, do not on their own explain the rich world of states of matter, however mutual interactions lead to various states or phases of matter.This work focuses on phases in quantum spin systems.On the basis of the Heisenberg model one (1D) and two dimensional (2D) spin lattices are investigated.In a first part the bilayer Heisenberg Model and the 2D Kondo necklace model are studied.Both models exhibit a quantum phase transition between an ordered and disordered phase.For small interlayer couplings the models have antiferromagnetic long-range order, which is destroyed by increasing the coupling.However, even in the disordered phase the models show global features in terms of collective excitations called magnons.Coming from the disordered phase the gapped magnons condense at a critical coupling and form the order of the ordered phase.Here, another interesting question arises, namely that of the coupling of a single doped hole to such critical fluctuations.A self-consistent Born approximation predicts that the doped hole couples to the magnons such that the quasiparticle residue vanishes at the quantum critical point.In this work the delicate question about the fate of the quasiparticle residue across the quantum phase transition is also tackled by means of large scale quantum Monte Carlo simulations.Furthermore the dynamics of a single hole doped in the magnetic background is investigated.
We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many interesting properties due to large quantum fluctuations. As a result of these fluctuations usual mean-field approach gives quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive at investigations of such systems. The exact ground state wave function of proposed models has a structure of the valence-bond state (VBS) type. One of the 1D model describes the transition line between the F and AF phase. The exact singlet ground state on this line has a double-spiral ordering. Using different approximation methods we study the magnetization curve in the AF phase. The second considered set of the 1D and 2D models has an exact non-degenerate ground state with exponentially decaying spin correlations. We also proposed the 1D and 2D electronic models with exact ground state represented in terms of singlet bond functions which are the generalization of the RVB functions including ionic states.