Quasiconserved quantities in the perturbed spin- 12 XXX model

Abstract

We consider the isotropic spin-1 2 Heisenberg spin chain weakly perturbed by a local translationally and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasiconserved integrals of motion (charges) for the perturbed model. Such quasiconserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation the quasiconserved quantities indeed exist, and we construct an explicit form for the first few of them.

Anomalous transport from hot quasiparticles in interacting spin chains

“…In both classical and quantum systems in the thermodynamic limit, all initial conditions eventually lead to chaos, but the rate at which chaos sets in can be much slower than the naive Golden Rule estimate: this can happen, e.g. because some parts of the perturbation can be absorbed into the unperturbed Hamiltonian through a unitary rotation [145,182]. The prospects for studying these phenomena in near-term simulations or experiments involving quantum spin chains are not very favorable, because of the rapid growth of entanglement and the late times required.…”

“…While the case of time-independent, Hamiltonian integrability-breaking perturbations (such as a next-nearest neighbor coupling) is much harder to study numerically, there has been interesting analytic progress on this problem [145]. The essential observation is that one can perform a unitary rotation U on H to extract HU(λ)HU † (λ) such that, to leading order in λ, H = H + λV where V is the integrability-breaking perturbation.…”

Formation of robust bound states of interacting microwave photons

“…One known exception is many-body scars, in which certain initial states exhibit periodic revivals and do not thermalize 30,31 . Moreover, in the case of weak integrability breaking, robustness to perturbations can result from quasi-conserved or hidden conserved quantities 32,33 . However, the resilience observed here extends well beyond the weak integrability breaking regime typically considered in such scenarios 34 .…”

Weak vs. strong breaking of integrability in interacting scalar quantum field theories

“…Integrability is related to the presence of higher conserved charges, which generally make the number of (quasi)particle excitations conserved as they restrict the set of incoming and outgoing momenta to be the same in any multi-particle scattering process and also restrict all amplitudes to the product of independent two-particle amplitudes [4,5]. Integrability breaking perturbations lead to violations of the higher conservation laws, with weak integrability breaking being characterised by breaking them at higher order in the coupling parameter [6][7][8][9][10][11].…”