Microscopic resonant-shell mechanism for slow Liouvillian sectors in an open correlated lattice

TL;DR

This paper presents a microscopic theory explaining how slow Liouvillian sectors emerge in an open correlated lattice through local resonances and shell dynamics, revealing new mechanisms for reservoir-engineered slow modes.

Contribution

It introduces a microscopic framework based on local resonances and shell projections to understand slow Liouvillian sectors in open quantum systems.

Findings

Identifies a local shell resonance controlling slow sector selection.

Derives a boundary doublon-loss channel leading to exponential slow dynamics.

Reveals a shell-critical point with algebraic spacing and density dressing effects.

Abstract

We develop a microscopic theory for how slow Liouvillian sectors are selected in an open correlated lattice. The starting point is not a postulated non-Hermitian band, but a local interacting resonance between an on-site doublon and a branch-resolved nearest-neighbor bond. This resonance defines a composite shell orbital whose doublon weight controls reservoir visibility and whose mixed doublon-bond character controls shell mobility. Projecting the microscopic hopping onto the selected shell yields a branch-selective dimerized channel. In the dilute regime, a boundary doublon-loss channel yields an exponentially slow edge-memory pole through a Zeno-type return. At the shell-critical point, the edge pole is replaced by a near-zero standing-wave doublet with an algebraic coherent spacing. At finite shell filling, the same local shell becomes density dressed. A number-conserving phase-locking jump removes a bright mismatch sector, leaving defects as the asymptotic slow variables and producing a diffusive finite-size gap. We derive the local shell, the projected branch topology, the edge-memory law, the shell-critical doublet, the density-dressed shell Hamiltonian, and the defect generator within one Schur-projection framework. The resulting mechanism identifies the reservoir-engineered fast block as the selector of the observable slow sector, while the microscopic parent shell remains fixed.