We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an offdiagonal exchange Γ and isotropic third-nearest-neighbor interaction J3 on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides α-Li2IrO3 and Na2IrO3, and Ru-based materials such as α-RuCl3. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is Γ = K > 0, where K is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra. arXiv:1911.12829v1 [cond-mat.str-el]

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. This flow allows for an understanding of the surprising role of critical slowing down at a quantum first-order transition in strongly-correlated electronic systems. From a simple truncation of the infinite hierarchy of the exact functional RG flow equations we identify several fixed points: Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum firstorder transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of this quantum first-order transition in terms of a local effective Ising variable that is established for classical transitions. It reveals that quantum phase coexistence can be a genuine critical state of matter.

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of ∼ 0.6. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of Cs2CuBr4 and Cs2CuCl4 we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields. arXiv:1911.09403v1 [cond-mat.str-el]

We show that the single-particle Green's functions used in many body theory have an elegant description in the form of hyperfunctions. We summarize the necessary hyperfunction concepts. We show that the analytical properties and the relations between different Green's functions are natural within this formulation. Important results from the standard formalism are recovered straightforwardly. We argue that hyperfunctions could possibly provide a powerful new tool for many body theory, if the formalism could be developed beyond single-particle Green's functions.