The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the RV O(3) perovskites, with R = La,Pr,…,Y b,Lu, where the finite temperature properties of these compounds can be understood only using entangled states: (i) the thermal evolution of the optical spectral weights, (ii) the dependence of the transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the RV O(3) perovskites, and (iii) the dimerization observed in the magnon spectra for the C-type antiferromagnetic phase of Y V O(3). Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduce topological constraints for the hole propagation and will thus radically modify the transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.

In this work, we address the ground-state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases—antiferromagnetic, paramagnetic, and chiral—and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.

Systems containing the ideal kagome lattice can exhibit several distinct and novel exotic states of matter. One example of such systems is a recently discovered $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) family of compounds. Here the coexistence of the charge density wave (CDW) and superconductivity is observed. In this paper, we study the dynamic properties of the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ systems in context of origin of the CDW phase. We show and discuss the structural phase transition from $P6/mmm$ to $C2/m$ symmetry that is induced by the presence of phonon soft modes. We conclude that the CDW observed in this family of compounds is a consequence of the atom displacement, from the high-symmetry position of the kagome net, in the low-temperature phase. Additionally, using the numerical ab initio methods, we discuss the charge distribution on the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ surface. We show that the observed experimental stripelike modulation of the surface can be related to surface reconstruction and manifestation of the three-dimensional $2\times 2\times 2$ bulk CDW. Finally, the consequence of realization of the $C2/m$ structure on the electronic properties is discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.

The recently discovered heavy fermion ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ compound crystallizes in nonsymmorphic $P4/nmm$ symmetry, which enables the occurrence of topological protection. Experimental results show that this material exhibits unusual behavior, which is manifested by the appearance of two superconducting phases. In this Letter, we uncover and discuss the role of ${\mathrm{Rh}}_2{\mathrm{As}}_2$ layers and their impact on the electronic and dynamical properties of the system. The location of Ce atoms between two nonequivalent layers allows for the realization of orbital order. We point out that the electronic band structure around the Fermi level is associated mostly with Ce $4f$ and Rh $4d$ orbitals and suggest the occurrence of the Lifshitz transition induced by an external magnetic field. We discuss also the role played by the $f-d$ orbital hybridization in the electronic band structure.

To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $|{\mathbb{Z}}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\varphi$, where the Kitaev term is $K\equiv sin\left(\varphi \right)$ and competes with the Heisenberg $J\equiv cos\left(\varphi \right)$ term. One finds a rich ground-state phase diagram as a function of the angle $\varphi$. Depending on the ratio $K/J\equiv tan\left(\varphi \right)$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin-liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey ${\mathbb{Z}}_2$-symmetry, while it becomes unstable against Heisenberg-type perturbations.