Condensed Matter Physics Seminar

Ergodicity hypothesis – a cornerstone of statistical mechanics -- is known to break in classical "integrable" systems, characterized by the presence of integrals of motion. In quantum world, ergodicity can be violated in disordered systems: a single particle moving in disorder potential can get trapped in some spatial region – a phenomenon known as Anderson localization. Recently, it was shown that localization can exist more generally in disordered quantum systems of interacting particles, giving rise to a many-body localized phase.

In this talk, I will present a theory of the many-body localized (MBL) phase. The key insight comes from the remarkably simple entanglement structure of excited MBL eigenstates, which satisfy so-called area-law (similar to ground states of gapped systems).  We use this property to show the existence of an infinite number of emergent local conservation laws [1]. The local integrals of motion can be viewed as quantum bits which cannot decay, but do dephase. We argue that, in terms of these "qubits", Hamiltonian has a universal form, giving rise to universal dynamical properties of MBL phase [1]. In particular, for initial product states, we predict (i) experimentally observable power-law decay of local observables to their long-time values, and (ii) logarithmic in time spreading of entanglement [2,3], which comprises a new regime of information propagation in many-body systems. 

I will propose numerical methods to obtain the integrals of motion and the universal Hamiltonian. Finally, I will discuss experimental implications of our theory, and explore the possibility of MBL in translationally invariant many-body systems.