Theoretical Physics Technical Talk

In this talk, I will describe how quantum noise leads to genuinely non-equilibrium patterns of quantum criticality. I study the effects of local measurements and noise on the toric code groundstate [13], which is topologically ordered, long-range entangled, and realises a quantum error-correcting code. Varying the local error probability leads to a noise-induced phase transition that coincides with the error-correction threshold. Such phase transitions separate distinct mixed state phases of matter, which are sharply diagnosed via their information theoretic properties, namely, the conditional mutual information (CMI). The CMI defines a mixed state equivalent of the correlation length, called the “Markov length”, which diverges at this noise-induced phase transition. Furthermore, for the toric code under a particular error model, I demonstrate the existence of an extended non-equilibrium critical phase. The universal properties of the phases and the phase transitions can be mapped to a classical statistical mechanical model of loop packing on the square lattice.

Crucially, the divergence of Markov length distinguishes such noise-induced phase transitions from thermal phase transitions, where it always remains finite - a hallmark of equilibrium. We uncover subtle signatures of such genuinely non-equilibrium criticality even in equilibrium thermal states. We study marginals of thermal Gibbs states along sub dimensional manifolds, such as their physical boundaries. While the bulk Markov length remains finite at thermal phase transitions, we show that the boundary Markov length generically diverges at bulk phase transitions [4]. Furthermore, we relate the universal properties of the CMI to non-standard probes of the conformal field theory (CFT) describing these transitions, with Ising and compact boson CFTs as our primary examples.

[1] Negari, SS, Hsieh ArXiv 2307.02292 (PRB 2024)

[2] Negari, SS, Behrends, Béri, Hsieh Arxiv 2601.10792 (PRX Quantum, to appear)

[3] Negari, SS, Behrends, Béri, Hsieh (in preparation)

[4] SS, Zou, Hsieh (in preparation)