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arXiv:cond-mat/9912099 · Physical review. B, Condensed matter

Hole dynamics and photoemission in a t−J model for SrCu2(BO3)2

Matthias Vojta C

Published May 1, 2000• 3 citations
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Abstract

The motion of a single hole in a $t\ensuremath{-}J$ model for the two-dimensional spin-gap compound ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a N\'eel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the interdimer hopping parameters we find a crossover between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the N\'eel-ordered phase is also briefly considered.

DOI
10.1103/physrevb.61.11309

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The motion of a single hole in a t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model for the two-dimensional spin-gap compound SrCu2(BO3)2{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a N'eel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the interdimer hopping parameters we find a crossover between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the N'eel-ordered phase is also briefly considered.
The two-layer square lattice quantum antiferromagnet with spins 12\frac{1}{2}21​ shows a magnetic order-disorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a $t\ensuremath{-}J$ Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system that covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics on both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The crossover between these two scenarios occurs inside the antiferromagnetic phase, which indicates that the hole dynamics is governed by the local environment of the hole.
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.
We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional t1,2,3{t}_{1,2,3}t1,2,3​-J1,2,3{J}_{1,2,3}J1,2,3​ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.
We investigate quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ by using the series expansion method. It is found that a novel spin-gap phase, adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known thus far. When the ratio of the competing exchange couplings $\ensuremath{\alpha}({\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}J}^{\ensuremath{'}}/J)$ is varied, this spin-gap phase exhibits a first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point ${\ensuremath{\alpha}}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.677(2)$ [ ${\ensuremath{\alpha}}_{c2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.86(1)$]. Our results shed light on some controversial arguments about the nature of quantum phase transitions in this model.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on La1.28Nd0.6Sr0.12CuO4.{\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.La1.28​Nd0.6​Sr0.12​CuO4​.
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.