A previous work (Joshi et al., arXiv:1912.08822) found a deconfined critical point at non-zero doping in a $t$-$J$ model with all-to-all and random hopping and spin exchange, and argued for its relevance to the phenomenology of the cuprates. We exten
d this model to include all-to-all and random density-density interactions of mean-square strength $K$. In a fixed realization of the disorder, and for specific values of the hopping, exchange, and density interactions, the model is supersymmetric; but, we find no supersymmetry after independent averages over the interactions. Using the previously developed renormalization group analysis, we find a new fixed point at non-zero $K$. However, this fixed point is unstable towards the previously found fixed point at $K=0$ in our perturbative analysis. We compute the exponent characterizing density fluctuations at both fixed points: this exponent determines the spectrum of electron energy-loss spectroscopy.
Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts
a time-reversal-symmetry protected $mathbb{Z}_2$ topological quantum paramagnet ({em topological triplon insulator}) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial $mathbb{Z}_2$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the $mathbb{Z}_2$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the $mathbb{Z}_2$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d$^{4}$ Mott insulators, and their potential applications.
With the advancement in synthesizing and analyzing Kitaev materials, the Kitaev-Heisenberg model on the honeycomb lattice has attracted a lot of attention in the last few years. Several variations, which include additional anisotropic interactions as
well as response to external magnetic field, have been investigated and many exotic ordered phases have been discussed. On the other hand, quantum spin systems are proving to be a fertile ground to realize and study bosonic analogues of fermionic topological states of matter. Using the spin-wave theory we show that the ferromagnetic phase of the extended Kitaev-Heisenberg model hosts topological excitations. Along the zig-zag edge of the honeycomb lattice we find chiral edge states, which are protected by a non-zero Chern number topological invariant. We discuss two different scenarios for the direction of the spin polarization namely $[001]$ and $[111]$, which are motivated by possible directions of applied field. Dynamic structure factor, accessible in scattering experiments, is shown to exhibit signatures of these topological edge excitations. Furthermore, we show that in case of spin polarization in $[001]$ direction, a topological phase transition occurs once the Kitaev couplings are made anisotropic.
It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily b
e manipulated by an applied field. Here we study triplon excitations in an S=1/2 quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By the bulk-boundary correspondence, we find that the non-zero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.
