Emergent eigenstate solution to quantum dynamics

Geoffrey L. Price, Baker, B. Mitchell, Palle E. T. Jørgensen +1 more

Lev Vidmar, Wei Xu, Marcos Rigol

Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble).

Yicheng Zhang, Lev Vidmar, Marcos Rigol

Generalized thermalization is a process that occurs in integrable systems in which unitary dynamics, e.g., following a quantum quench, results in states in which observables after equilibration are described by generalized Gibbs ensembles. Here we discuss an emergent eigenstate construction that allows one to built emergent local Hamiltonians of which one eigenstate captures the entire generalized thermalization process following a global quantum quench. Specifically, we study the emergent eigenstate that describes the quantum dynamics of hard-core bosons in one dimension for which the initial state is a density wave, and this state evolves under a homogeneous Hamiltonian.

Lev Vidmar, Deepak Iyer, Marcos Rigol

Quantum systems that are far from equilibrium can exhibit strange behavior, such as the emergence of coherence in an expanding Bose gas in an optical lattice. A theoretical analysis provides new insight into this phenomenon and a toolkit for understanding a wide range of similar phenomena.

D. C. Hutcgings