Slowest local operators in quantum spin chains.
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion. Then we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically "trivial," with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.
Physics Department, Princeton University, Princeton, New Jersey 08544, USA.|Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA.
Hyungwon
H
Kim
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany.
Mari Carmen
MC
Bañuls
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany.
J Ignacio
JI
Cirac
Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA.|Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
Matthew B
MB
Hastings
Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
David A
DA
Huse