We study the tunneling dynamics of dopant-induced hole polarons that are self-localized by electron-phonon coupling in a two-dimensional antiferromagnet. Our treatment is based on a path-integral formulation of the adiabatic (Born-Oppenheimer) approximation, combined with many-body tight-binding, instanton, constrained lattice dynamics, and many-body exact diagonalization techniques. The applicability and limitations of the adiabatic approximation in polaron tunneling problems are discussed in detail and adiabatic results are compared to exact numerical results for a two-site polaron problem. Our results are mainly based on the Holstein- $\mathrm{tJ}$ and, for comparison, on the Holstein-Hubbard model. We also study the effects of second-neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian that takes the form of a fermion tight-binding model with occupancy-dependent, predominantly second- and third-neighbor tunneling matrix elements, excluded double occupancy, and effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the first-neighbor charge interaction and by Berry phase factors that determine the signs of effective polaron tunneling matrix elements. In the two-polaron case, these phase factors lead to polaron-pair wave functions of either ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry or p-wave symmetry with zero and nonzero total pair momentum, respectively. Implications for the doping-dependent isotope effect, pseudogap, and ${T}_{c}$ of a superconducting polaron-pair condensate are discussed and compared to observed properties of the cuprate high- ${T}_{c}$ materials.We study the tunneling dynamics of dopant-induced hole polarons that are self-localized by electron-phonon coupling in a two-dimensional antiferromagnet. Our treatment is based on a path-integral formulation of the adiabatic (Born-Oppenheimer) approximation, combined with many-body tight-binding, instanton, constrained lattice dynamics, and many-body exact diagonalization techniques. The applicability and limitations of the adiabatic approximation in polaron tunneling problems are discussed in detail and adiabatic results are compared to exact numerical results for a two-site polaron problem. Our results are mainly based on the Holstein-$\mathrm{tJ}$ and, for comparison, on the Holstein-Hubbard model. We also study the effects of second-neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian that takes the form of a fermion tight-binding model with occupancy-dependent, predominantly second- and third-neighbor tunneling matrix elements, excluded double occupancy, and effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the first-neighbor charge interaction and by Berry phase factors that determine the signs of effective polaron tunneling matrix elements. In the two-polaron case, these phase factors lead to polaron-pair wave functions of either ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry or p-wave symmetry with zero and nonzero total pair momentum, respectively. Implications for the doping-dependent isotope effect, pseudogap, and ${T}_{c}$ of a superconducting polaron-pair condensate are discussed and compared to observed properties of the cuprate high-${T}_{c}$ materials.

arXiv:cond-mat/9805320Physical review. B, Condensed matterJan 1, 19995 citations

Berry phase and quantum structure

Holger Lyre

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern PhysicsOct 7, 20148 citations

Geometric (Berry) phases and statistical transmutation in the two-dimensional systems of strongly correlated electrons

Seung-Pyo Hong, Sung‐Ho Suck Salk

Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine geometric phases acquired by electronic wave functions as a result of polaron transport around a closed loop. For this study we apply the Lanczos exact diagonalization method to Holstein-Hubbard, Holstein- $tJ$ , and Holstein- $tJ_z$ models in order to reveal various aspects of geometric phases. We demonstrate that transverse spin fluctuations are responsible for the generation of nontrivial geometric phases. From the exchange symmetry of polarons we find that the statistical transmutation of polarons occurs depending on the strength of electron correlations.Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine geometric phases acquired by electronic wave functions as a result of polaron transport around a closed loop. For this study we apply the Lanczos exact diagonalization method to Holstein-Hubbard, Holstein-$tJ$, and Holstein-$tJ_z$ models in order to reveal various aspects of geometric phases. We demonstrate that transverse spin fluctuations are responsible for the generation of nontrivial geometric phases. From the exchange symmetry of polarons we find that the statistical transmutation of polarons occurs depending on the strength of electron correlations.

arXiv:cond-mat/9902094Feb 8, 19990 citations

The Relevance of Berry Phase in Quantum Physics

Pratul Bandyopadhyay

Statistical science and interdisciplinary researchNov 1, 20090 citations

\mathrm{tJ}

and, for comparison, on the Holstein-Hubbard model. We also study the effects of second-neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian that takes the form of a fermion tight-binding model with occupancy-dependent, predominantly second- and third-neighbor tunneling matrix elements, excluded double occupancy, and effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the first-neighbor charge interaction and by Berry phase factors that determine the signs of effective polaron tunneling matrix elements. In the two-polaron case, these phase factors lead to polaron-pair wave functions of either ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry or p-wave symmetry with zero and nonzero total pair momentum, respectively. Implications for the doping-dependent isotope effect, pseudogap, and

{T}_{c}

of a superconducting polaron-pair condensate are discussed and compared to observed properties of the cuprate high-

{T}_{c}

materials.

tJ

, and Holstein-

tJ_z

models in order to reveal various aspects of geometric phases. We demonstrate that transverse spin fluctuations are responsible for the generation of nontrivial geometric phases. From the exchange symmetry of polarons we find that the statistical transmutation of polarons occurs depending on the strength of electron correlations.