Emergent eigenstate solution to quantum dynamics

One of the main theoretical goals in studies of far-from-equilibrium dynamics of quantum many-body systems is to design accurate tools to predict the time evolution of physical observables. However, another important goal, well-aligned with the recent experimental efforts, is to pave way towards efficient manipulation of quantum many-body states. It is therefore highly desirable to make steps beyond the "predictable" quantum dynamics and to establish novel tools for "controllable" quantum dynamics. I am going to show that the emergent eigenstate solution to quantum dynamics [1] provides an important step in this direction.

The cornerstone of the emergent eigenstate solution is the construction of an emergent local Hamiltonian, an explicitly time dependent operator, of which time-evolving pure states are eigenstates. The crucial property of the emergent Hamiltonian is locality: in fact, even for solvable models, this is generically not the case. I am going to present experimentally relevant examples of quantum quenches in two families of one-dimensional lattice models (quadratic fermionic models including hard-core bosons, and the anisotropic Heisenberg spin-1/2 model), where the emergent local Hamiltonian can be constructed [1,2]. I am also going to show that the emergent local Hamiltonian can be constructed for initial mixed states, giving rise to the emergent Gibbs ensemble to describe quantum dynamics [2].

Finally, I am going to show an example suggesting that the emergent eigenstate solution can be used as a tool to achieve shortcuts to adiabaticity [3]. For isolated noninteracting and weakly interacting fermionic systems, I am going to study how to adiabatically transfer the initial state from linear or harmonic traps into a box trap. A quantum adiabatic protocol will be presented which gives rise to a controllable speed up if the emergent local Hamiltonian is included in the protocol.

[1] PRX 7, 021012 (2017)
[2] PRA 96, 013608 (2017)
[3] PRE 96, 042155 (2017)