Channeling quantum criticality

TL;DR

This paper studies how local decoherence affects quantum critical states, revealing universal entanglement properties, RG flows, and scaling behaviors, with implications for noisy quantum simulators.

Contribution

It introduces a universal framework connecting decoherence effects on quantum critical states to conformal field theory and RG flow, with numerical verification in the transverse-field Ising model.

Findings

Renyi entropies follow volume law with a g-function governed subleading term.

Subsystem entropy exhibits logarithmic scaling related to boundary condition changes.

Entanglement negativity can switch between log scaling and area law depending on RG flow.

Abstract

We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "$g$-function" in conformal field theory (CFT), allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the CFT. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.