The longest-lived current in a quantum chaotic spin chain

To explore issues of numerically capturing dissipative dynamics in closed many-body quantum systems, we have studied the relaxation of nonconserved current operators in a certain quantum chaotic spin chain. The Hamiltonian is a translationally-invariant spin-1/2 chain with nearest-neighbor XY interactions and a tilted field that breaks the conservation of total Z magnetization. We look at an infinite chain and examine the relaxation of all “current” operators that have total momentum zero and are odd under spatial inversion. The relaxation is via operator spreading: a unitary flow in operator space from simple short Pauli strings to long (and thus nonlocal) Pauli strings. To approximate this numerically, we limit the length of the Pauli strings and introduce an artificial nonunitary damping that acts only on the longest Pauli strings that we keep, and solve exactly for the longest-lived current operator in this approximation. We find that there is a regime of this artificial damping where we obtain a good approximation to the correct unitary dynamics, while in other regimes the artificial damping causes a blockage of the proper unitary flow in operator space and, as a result of this “bad plumbing”, gives incorrect results.