Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with $t_{2g}$ orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with $t_{2g}$ orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.

arXiv:0811.3765Nov 24, 20080 citations

A SELF-CONSISTENT ANALYTIC THEORY OF THE SPIN BIPOLARON IN THE t–J MODEL

H. Barentzen, V. S. Oudovenko

The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.

International Journal of Modern Physics BMar 30, 20000 citations

Spatial structure of spin polarons in the t−J model

A. Ramšak, Peter Horsch

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 $J$ as small as $0.1t$ . 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.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 $J$ as small as $0.1t$. 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.

arXiv:cond-mat/9712119Physical review. B, Condensed matterFeb 15, 199843 citations

Spin polarons in the t - J model

Gerardo Martı́nez, Peter Horsch

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 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.

Physical review. B, Condensed matterJul 1, 1991498 citations

Spin polarons in thet-Jmodel: Shape and backflow

A. Ramšak, Peter Horsch

The self-consistent Born approximation for the self-energy and the wave function of a single hole moving in a two-dimensional quantum antiferromagnet is used to calculate various spin-correlation functions that characterize the perturbation induced by the hole. The results for these correlation functions agree with the available small-cluster calculations. The hole-spin correlation functions decay asymptotically with the distance from the hole as a power law and exhibit a dipolar distortion of the antiferromagnet. The quasiparticle spectral weight remains finite.The self-consistent Born approximation for the self-energy and the wave function of a single hole moving in a two-dimensional quantum antiferromagnet is used to calculate various spin-correlation functions that characterize the perturbation induced by the hole. The results for these correlation functions agree with the available small-cluster calculations. The hole-spin correlation functions decay asymptotically with the distance from the hole as a power law and exhibit a dipolar distortion of the antiferromagnet. The quasiparticle spectral weight remains finite.

Physical review. B, Condensed matterOct 1, 199352 citations

Spin polarons in triangular antiferromagnets

Matthias Vojta C

The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the $t\ensuremath{-}J$ model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large $J/t$ we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small $J/t$ this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the $t\ensuremath{-}J$ model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large $J/t$ we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small $J/t$ this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.

arXiv:cond-mat/9811191Physical review. B, Condensed matterMar 1, 199915 citations

Reiter's polaron wavefunction applied to a

t_{2g}

orbital t-J model

Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with

t_{2g}

orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.

J

as small as

0.1t

. 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.

J/t

we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small

J/t

this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.