# Research & Annual Reports

The Theory of Quantum Matter (TQM) Unit carries out research into a wide range of problems in condensed matter theory, with a strong emphasis on the novel phases and excitations found in quantum matter.

This work is described in the **Annual Reports** listed in the menu on the left side of this page. These provide details of all of the research carried out by the TQM Unit, publications and presentations by Unit members, outreach activity, and seminars given by visitors to TQM in OIST. Reports are organised by the Japanese financial year, with FY2019 running from **April 1**^{st}** 2019** until **March 31**^{st}** 2020**.

Results which appeared since March 31st, 2020, are described below:

### 1. Emergence of a nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

The interplay of competing interactions and quantum fluctuations in spin systems can give rise to new and exciting physics. A prominent realisation with these competing interaction are Kitaev materials, which exhibit strong spin-orbit coupling leading to bond-dependent interactions between spin-1/2 constituents. If the Kitaev interaction is dominant, these materials have the potential to realize a quantum spin liquid phase. However, many such materials have additional interactions that stabilize magnetically ordered states. A paradigmatic example is \alpha-RuCl3, which is known to stabilize zigzag magnetic order. Upon applying a magnetic field, however, the zigzag order vanishes, while recent thermal Hall conductivity measurements indicate the existence of the much-desired Kitaev spin liquid. Consequently, Kitaev materials exposed to an external magnetic field have recently been a subject of intensive studies.

In this work, we investigate the Kitaev-Gamma-Gamma' model which has been suggested as a minimal model for \alpha-RuCl3. By using matrix product state techniques and linear spin wave theory, we show that a nematic paramagnet emerges in the quantum model in a magnetic field along the [111] direction. The nematic paramagnet is characterized by a spontaneous breaking of a lattice-rotational symmetry. We trace its origin to the frustrated ferromagnetic phase of the corresponding classical model. A homogeneous canting of the magnetic moments away from the field axis occurs as a result of a competition between the magnetic field and the anisotropic spin-exchange couplings. Classically, no preferred canting direction exists resulting in a continuous, U(1)-symmetric, manifold of ground states. A mechanism known as quantum order-by-disorder selects a discrete set of states, the nematic paramagnetic states, out of an emergent continuous manifold of ground states in the classical model. The continuous symmetry implies a gapless Nambu-Goldstone mode, however, quantum fluctuations introduce a small gap. Such a phenomenology has become known as a pseudo-Goldstone mode.

The nematic paramagnet exists in a wide range of parameters. Thus, this phase is likely relevant to \alpha-RuCl3 and possibly other Kitaev materials. Consequently, we complement our work by presenting dynamical signatures, i.e. the dynamical spin structure factor, of the nematic paramagnet and the adjacent high-field paramagnet. Although we find the Kitaev spin liquid to be stabilized only in the vicinity of pure Kitaev coupling, remnants of the fractional excitations of the KSL continue to exist in wider range of parameters illustrating a proximate spin liquid.

In summary, this work elucidates the origin of a nematic paramagnetic phase that is stabilized in a wide range of parameters relevant to Kitaev materials, and presents dynamical signatures that are potentially relevant to understand recent experiments on Kitaev materials.