My Research

Spacetime duality: 

The theory of relativity tells us that time is just a direction like those in space. This insight allows one to perform many calculations in such theories by thinking of a spatial direction as a time direction and vice versa. Amazingly, this perspective can be employed in systems that are not relativistic, like lattice systems. Space-time duality is an approach to quantum dynamics that avails of this fact. It is particularly powerful for integrable models where you can use exact solutions in equilibrium problems to get exact solutions to non-equilibrium ones. 

[Physical Review Letters 131 (14), 140401,Physical Review B 109 (18), 184312]

Entanglement and symmetry dynamics in the presence of local defects: 

If I prepare a state that breaks a certain symmetry and evolve it under symmetric dynamics, it is expected that the symmetry is restored locally. If however, the symmetry of the dynamics is broken by a local perturbation, is it still possible to restore the symmetry or does a single perturbation ruin everything? 

[Physical Review Letters 131 (15), 156303, Physical Review B 112 (6), 064305]  

Measurements in integrable models: 

When unitary dynamics are interspersed with projective measurements, a competition ensues between relaxation to the stationary state of the dynamics or the measurements. This leads to many interesting transitions which have been studied extensively from a number of angles. By using integrable dynamics which have an large number of conserved quantities and making extended measurements of these quantities, one can gain analytic insight into these hybrid systems. 

[Physical Review A 109 (4), 043302]