Emergent eigenstate solution to quantum dynamics

Lev Vidmar, Institut Jozef Stefan in Ljubljana, Slowenien

12.01.2018 at 09:00 

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 c onstructed 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 r ise to a controllable speed up
if the emergent local Hamiltonian is included in the protocol.
[1] Vidmar, Iyer, Rigol, PRX 7, 021012 (2017)
[2] Vidmar, Xu, Rigol, PRA 96, 013608 (2017)
[3] Modak, Vidmar, Rigol, PRE 96, 042155 (2017)