The distinguishing feature of a quantum material is that a classical macroscopic description is unsatisfactory and the bulk properties can only be obtained by invoking quantum mechanics at higher energies and larger length scales than usually required for describing the fundamental interactions between isolated electrons and atoms. Examples of large scale quantum effects include phenomena such as superconductivity and superfluidity and quantum effects are responsible for the unique features that occur in materials identified as topological insulators and spin ices among others. Dynamic quantum matter refers to any type of matter that requires both a quantum mechanical and time-dependent treatment.

Most traditional theoretical approaches to describing materials assume that the system in question is held in equilibrium, which simplifies calculations by removing all time-dependence from the system. Dynamical aspects have to be considered when one or more of external driving (excitation), internal dynamics, inherent fluctuations or dissipation to an environment are included. In addition, other systems that include or allow unusual behaviour under reordering or variation of time labels can also require dynamical factors to be included in any discussion.

Excitation is often realised in experiments, either as continuous or pulsed protocols, and will be crucial in the vast majority of potential applications. Internal dynamics are always present and energy relaxation protocols are used to find the ground state in equilibrium studies. Dissipation can be difficult to include since this is often experimentally uncontrolled; a Markovian heat bath is an analytically tractable example. Analysing the quantum or thermal fluctuations that occur near a phase transition help understand which interactions are important (e.g.: via renormalisation group), but may also have their own signatures.

Research in the group considers three realisations of dynamical quantum matter:

- Dynamical multiferroicity: The Dzyaloshiksii-Moriya interaction leads to an effective polarisation from a static spin spiral; exploiting the duality between electricity and magnetism in Maxwell’s equations, a complementary effect –
**Dynamical Multiferroicity**– is possible. - Pumped Dirac materials: Pump-probe experiments have demonstrated that Dirac materials may be driven into transient excited states with two chemical potentials, one for the electrons and one for the holes, which effectively offers control of the strength of the Coulomb interaction.
- Odd frequency superconductivity: Most theories of superconductivity consider the limit of equal-time pairing, however, electrons may also be paired at unequal times which leads to superconducting gaps that can be odd in time or, equivalently, frequency.