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Physical review. B, Condensed matter

Quasiparticle band structure of a hole in a quantum Heisenberg antiferromagnet

Jean‐Louis Richard, V. Yu. Yushankhaï

Published Jan 1, 1993• 23 citations
Publisher

Abstract

The problem of the single-hole motion in a two-dimensional quantum Heisenberg antiferromagnet is examined in the t-J model. By introducing a kind of slave-fermion representation for Hubbard operators a hole is treated as a spinless fermion strongly interacting with spin-1/2 degrees of freedom. We suggest an analytic approach based on a decoupling procedure for two-time fermionic Green functions that allows us to describe a hole as a magnetic polaron of a minimal size (i.e., involving one-step ``string'' spin excitations) and reproduce the main features characteristic of a one-hole band in a quantum antiferromagnet. A generalization of the procedure in the spirit of the Lanczos approach to extend the internal structure of the magnetic polaron is discussed.

DOI
10.1103/physrevb.47.1103

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International Journal of Modern Physics B•Jan 1, 1991•12 citations
The problem of the single-hole motion in a two-dimensional quantum Heisenberg antiferromagnet is examined in the t-J model. By introducing a kind of slave-fermion representation for Hubbard operators a hole is treated as a spinless fermion strongly interacting with spin-1/2 degrees of freedom. We suggest an analytic approach based on a decoupling procedure for two-time fermionic Green functions that allows us to describe a hole as a magnetic polaron of a minimal size (i.e., involving one-step ``string'' spin excitations) and reproduce the main features characteristic of a one-hole band in a quantum antiferromagnet. A generalization of the procedure in the spirit of the Lanczos approach to extend the internal structure of the magnetic polaron is discussed.
The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.
The motion of a single hole in an arbitrary magnetic background is investigated for the two-dimensional $t\ensuremath{-}J$ model. The wave function of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large-string basis for the limits of a N\'eel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature.
Abstract The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decades because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green’s function in the t–J model, where the J term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called string excitations found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy–momentum dependence of the main quasiparticle peak and its residue, the internal excitations of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.
Motion of a single hole is studied at finite temperatures in the t-J model on a slave-fermion Schwinger-boson representation. The spin fluctuation is treated with the mean-field theory of Arovas and Auerbach. The Green's function for the slave fermion is calculated within the self-consistent Born approximation. A sharp quasiparticle peak is found to be separated from a broad spectrum of incoherence in the spectral function for low temperatures. The Green's function for the physical hole is calculated by taking account of the multiple scattering between the slave fermion and the Schwinger boson. A bound state of the slave fermion and the Schwinger boson is found at low temperatures, suggesting that the spin and the charge cannot be separated into a simple form. The energy of the bound state is minimized at momenta (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2, \ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), indicating that a small pocketlike Fermi surface is formed around the momenta for low concentrations of dopant holes.
The deformation of the quantum N\'eel state induced by a spin polaron is analyzed in a slave fermion approach. Our method is based on the self-consistent Born approximation for the Green's function and wave function for the quasiparticle. The results of various spin-correlation functions relative to the position of the moving hole are discussed and shown to agree with those available from small cluster calculations. Antiferromagnetic correlations in the direct neighborhood of the hole are reduced, but they remain antiferromagnetic even for JJJ as small as 0.1t0.1t0.1t. These correlation functions exhibit dipolar distortions in the spin structure, which sensitively depend on the momentum of the quasiparticle. Their asymptotic decay with the distance from the hole is governed by power laws, yet the spectral weight of the quasiparticles does not vanish.
We solved numerically the integral equation for the selfenergy which describes the motion of a single hole in a two-dimensional quantum antiferromagnet (AF) within the selfconsistent Born approximation. This formulation stresses the similarity of the AF-spin polaron with the standard polaron problem. We confine our calculation to finite cluster geometries and compare with results from previous exact diagonalization studies. The spectral function is characterized by a narrow quasiparticle (qp) peak at the low energy side of the spectra, which appears to be well separated from the incoherent band part for large enough J values. For small J we find a reduced width of ~7t for the incoherent band. The bottom of the coherent qp band always occurs at (±π/2, ±π/2). Its bandwidth initially increases with J until J≃t and then decreases as 2t2/J. A complete characterization of our solution is given, including the dispersion relation and effective masses of this quasiparticle. The comparison with exact diagonalization studies for a 4×4 cluster is remarkably good. From our results we see that a lattice of 16×16 sites describes adequately the thermodynamic limit. We conclude that the simple Born approximation is a valuable scheme to characterize the dynamics of one hole in the t-J model. both in the perturbative and the strong coupling regimes.