Research Projects

The proposed research aims to explore the interplay of emergent symmetries and entanglement that are central to unconventional quantum phases and phase transitions. Ever growing list of materials and new hybrid quantum platforms provides a pressing need for comprehensive understanding of the above interplay with an eye to possible technological uses. A key ingredient is competing interactions that lead to kinetic constraints of the low energy many-body Hilbert space often with enhanced symmetries and entanglement which, then, govern the nature of the low energy excitations (spectra) and dynamics. The proposed research aims to understand these twin aspects using a combination of sophisticated analytical methods and powerful numerical simulations in a variety of such constrained interacting many-body systems that stabilise unconventional phases. The above situation is most clear in frustrated antiferromagnets whence magnetic moments are quenched via formation of local Bell pairs (spin singlets) or dimers - the low energy degrees of freedom - which then necessarily obey kinetic constraints akin to Gauss’s law of electromagnetism. Such description in terms of emergent electromagnetism (gauge theories) is the unifying language to describe the ensuing physics. The proposed research aims to understand such naturally constrained dimer models and associated gauge theories in three key naturally arising settings: The first objective is to explore the phase transition from a valence bond solid to a spin liquid in a triangular lattice dimer model. The goal is to identify emergent O(4) symmetry on a torus and find the possible instability of Dirac spin liquids in a triangular lattice by analysing low-energy spectra via extensive numerical exact diagonalisation and sign-free quantum Monte Carlo simulations of dual frustrated Ising model. Particularly, we propose to develop a systematic understanding of the lattice symmetries of the excitation spectra of the Ising magnetic flux — the vison. The second part examines a fermionic system coupled to Ising gauge fields on a square lattice, focusing on transitions between zero-flux and $\pi$-flux phases. The Hamiltonian involves competition between a gauge field term and a plaquette term, leading to interesting phase structure. The study includes computing fermion propagators in both phases and understanding how increasing fluctuations in the gauge field affects the phase diagram. Numerical tools such as Monte Carlo will be used for these investigations. Finally we plan to study the dynamics of a fermion in a fully packed dimer background on a square lattice. The fermion moves between nearest neighbour flippable plaquettes. The background dimer configuration evolves either classically (stochastically) or quantum mechanically via a Rokhsar-Kivelson Hamiltonian. Our plan is to find the dynamical regimes such as localization, diffusion or anomalous transport by probing the time-dependent spread of the fermion.