Bootstrapping Open Quantum Many-body Systems with Absorbing Phase Transitions

TL;DR

This paper introduces a bootstrap method leveraging positivity and steady-state conditions to analyze open quantum many-body systems with absorbing phase transitions, demonstrated on the quantum contact process.

Contribution

The authors develop a systematic bootstrap approach for studying open quantum systems governed by Lindblad equations, providing bounds on key physical quantities.

Findings

Obtained bootstrap bounds on steady-state expectation values.

Estimated the critical coupling for the quantum contact process.

Bound the Liouvillian spectral gap in the subcritical phase.

Abstract

We demonstrate that combining the positivity of density matrices with steady-state conditions yields a systematic bootstrap method for studying open quantum many-body systems governed by Lindblad master equations on infinite lattices, which exhibit absorbing phase transitions. As a concrete example, we apply this method to the quantum contact process with an absorbing state. We obtain bootstrap bounds on steady-state expectation values, the critical coupling, certain ratios of expectation values in the nontrivial steady state in the supercritical phase, and the Liouvillian spectral gap in the subcritical phase.