We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $Gamma$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic pr
operties of iridium oxides $alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $alpha$-RuCl$_3$. 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 $Gamma = K>0$, 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.
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 $sim0.6$. 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 $rm{Cs}_2rm{CuBr}_4$ and $rm{Cs}_2rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.
We report an experimental and theoretical study of the low-temperature specific heat $C$ and magnetic susceptibility $chi$ of the layered anisotropic triangular-lattice spin-1/2 Heisenberg antiferromagnets Cs$_2$CuCl$_{4-x}$Br$_x$ with $x$ = 0, 1, 2,
and 4. We find that the ratio $J/J$ of the exchange couplings ranges from 0.32 to $approx 0.78$, implying a change (crossover or quantum phase transition) in the materials magnetic properties from one-dimensional (1D) behavior for $J/J < 0.6$ to two-dimensional (2D) behavior for $J/J approx 0.78$ behavior. For $J/J < 0.6$, realized for $x$ = 0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, $C_{rm m} propto T$, consistent with spinon excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for $x$ = 2, where $J/J approx 0.78$ implies a 2D magnatic character, we also observe $C_{rm m} propto T$. This finding, which contrasts the prediction of $C_{rm m} propto T^2$ made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in frustrated spin-1/2 2D antiferromagnets.
We construct a new mean-field theory for quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equa
tions based on two-point correlation functions does not produce any unphysical finite-temperature phase transition in accord with Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.
We construct a many-body theory of magneto-elasticity in one dimension and show that the dynamical correlation functions of the quantum magnet, connecting the spins with phonons, involve all energy scales. Accounting for all magnetic states non-pertu
rbatively via the exact diagonalisation techniques of Bethe ansatz, we find that the renormalisation of the phonon velocity is a non-monotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons - via hybridisation with the continuum of excitations at high energy. We conduct ultrasonic measurements on a high-quality single crystal of the frustrated spin-1/2 Heisenberg antiferromagnet $textrm{Cs}_{2}textrm{CuCl}_{4}$ in its one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.
The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion redu
ces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $mathcal{R}^{2}/L^{2}$, where $mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.
Studying interacting fermions in 1D at high energy, we find a hierarchy in the spectral weights of the excitations theoretically and we observe evidence for second-level excitations experimentally. Diagonalising a model of fermions (without spin), we
show that levels of the hierarchy are separated by powers of $mathcal{R}^{2}/L^{2}$, where $mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.
A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles and between
Bose particles (with and without spin) using Bethe-Ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empirical model of a free, non-relativistic particle with an effective mass identified at low energies as the bare electron mass renormalised by the dimensionless Luttinger parameter $K$ (or $K_sigma$ for particles with spin). The relevance of the Luttinger parameters beyond the low energy limit provides a more robust method for extracting them experimentally using a much wide range of data from the bottom of the one-dimensional band to the Fermi energy. The empirical model of the spectral edge mode complements the mobile impurity model to give a description of the excitations in proximity of the edge at arbitrary momenta in terms of only the low energy parameters and the bare electron mass. Within such a framework, for example, exponents of the spectral function are expressed explicitly in terms of only a few Luttinger parameters.
Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a short range
interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation energy for a given momentum, is parabolic for arbitrary momenta and the prefactor is a function of the Luttinger parameter, K.
We study the polarisation dependence of the homogeneously broadened nuclear spin resonance in a crystal. We employ a combinatorial method to restrict the nuclear states to a fixed polarisation and show that the centre of the resonance is shifted line
arly with the nuclear polarisation by up to the zero polarisation line width. The width shrinks from its maximum value at zero polarisation to zero at full polarisation. This suggests to use the line shape as a direct measure of nuclear polarisation reached under dynamical pumping. In the limit of single quantum of excitation above the fully ferromagnetic state, we provide an explicit solution to the problem of nuclear spin dynamics which links a bound on the fastest decay rate to the observable width of the resonance line.
