Interacting SPT, duality and phase transition in dimerised XXZ spin-1/2 chain

In this talk, I shall discuss the physics of a one-dimensional spin-1/2 chain and in particular its unusually rich phase diagram that supports an interacting symmetry protected topological (SPT) phase, a spontaneously symmetry (that protects the SPT) broken phase and a trivial gapped phase-- all of which are separated by continuous phase transitions described by well known conformal field theories. The renormalisation group analysis leads to a class of double-frequency sine-gordon theory whoses fixed points describe the phase diagram of the microscopic model. The spin-model, interestingly, admits a lattice duality to deformed Quantum Ashkin-Teller model and this raises interesting questions about "hidden" symmetries and ensuing critical CFTs.