This paper considers an exact model of atomic spontaneous dipole emission and classical dipole radiation in a finite photonic bandgap (PBG) structure. The full three-dimensional (3-D) or two-dimensional (2-D) problem is reduced to a finite one-dimensional (1-D) model, which then is solved for analytically using algebraic matrix transfer techniques. The results give insight to the electromagnetic emission process in periodic dielectrics, quantitative predictions for emission in 1-D dielectric stacks, and qualitative formulas for the 2-D and 3-D problem.This paper considers an exact model of atomic spontaneous dipole emission and classical dipole radiation in a finite photonic bandgap (PBG) structure. The full three-dimensional (3-D) or two-dimensional (2-D) problem is reduced to a finite one-dimensional (1-D) model, which then is solved for analytically using algebraic matrix transfer techniques. The results give insight to the electromagnetic emission process in periodic dielectrics, quantitative predictions for emission in 1-D dielectric stacks, and qualitative formulas for the 2-D and 3-D problem.

arXiv:quant-ph/9906017Journal of Lightwave TechnologyNov 1, 199929 citations

Even-odd effect in multilayer Kitaev honeycomb magnets

Jaime Merino, Arnaud Ralko

Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer with an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction $J$ is analyzed through Abrikosov fermion mean-field theory. We find quantum spin liquid (QSL) solutions which are gapped (ungapped) for even (odd) number of layers. The presence (absence) of the gap in even- (odd-) layered systems is associated with the spontaneous breaking (nonbreaking) of the inversion symmetry of the multilayer by the mean-field QSL solution. The good agreement between the Gutzwiller projected mean-field energy and the exact energy at large $J$ indicates that our QSL solution is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and ${\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}$ which are examples of magnetically coupled multilayer Kitaev models.Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer with an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction $J$ is analyzed through Abrikosov fermion mean-field theory. We find quantum spin liquid (QSL) solutions which are gapped (ungapped) for even (odd) number of layers. The presence (absence) of the gap in even- (odd-) layered systems is associated with the spontaneous breaking (nonbreaking) of the inversion symmetry of the multilayer by the mean-field QSL solution. The good agreement between the Gutzwiller projected mean-field energy and the exact energy at large $J$ indicates that our QSL solution is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and ${\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}$ which are examples of magnetically coupled multilayer Kitaev models.

Physical review. B./Physical review. BFeb 27, 20251 citation

Three-Dimensional Potential Well

H. Bartel Williams

Physical ReviewSep 1, 19575 citations

Exact Solution of a Three-Dimensional Dimer System

H. Y. Huang, Vladislav Popkov, Fa Yueh Wu

We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. As an illustration of the general solution, we analyze the phase transitions in a realistic three-dimensional dimer system and determine its phase diagram and nature of transitions.We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. As an illustration of the general solution, we analyze the phase transitions in a realistic three-dimensional dimer system and determine its phase diagram and nature of transitions.

arXiv:cond-mat/9610184Physical Review LettersJan 20, 199713 citations

J

is analyzed through Abrikosov fermion mean-field theory. We find quantum spin liquid (QSL) solutions which are gapped (ungapped) for even (odd) number of layers. The presence (absence) of the gap in even- (odd-) layered systems is associated with the spontaneous breaking (nonbreaking) of the inversion symmetry of the multilayer by the mean-field QSL solution. The good agreement between the Gutzwiller projected mean-field energy and the exact energy at large

J

indicates that our QSL solution is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and

{\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}

which are examples of magnetically coupled multilayer Kitaev models.