Physics

Mathematical optimization

Hamiltonian (control theory)

Quasiparticle

Quantum state

Eigenvalues and eigenvectors

Quantum number

Ionization

Condensed matter physics

Mathematics

Mathematical physics

Superconductivity

Quantum mechanics

Rydberg formula

Quantum

Translational symmetry

Physical Review Letters

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body "scar states" showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite temperature} that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact $E = 0$ states) and open boundary conditions (two $E = 0$ states and one each $E = \pm \sqrt{2}$). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in one dimension at infinite temperature. We show that the nearby many-body scar states can be well approximated as "quasiparticle excitations" on top of our exact $E = 0$ scar states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain