Nambu-Goldstone Effective Theory of Information at Quantum Criticality

TL;DR

This paper establishes a link between quantum criticality in many-body systems and their ability to store and process information, using a new sigma model approach to analyze Goldstone modes as information carriers.

Contribution

It introduces a novel method mapping Bose-Einstein condensates onto sigma models to study quantum criticality and information dynamics, revealing parallels with black hole information processing.

Findings

Goldstone modes become gapless at criticality, acting as information carriers.

Information capacity scales exponentially or as a power law with particle number N.

Information storage longevity and scrambling time scale favorably with N.

Abstract

We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point we develop a new method by mapping a Bose-Einstein condensate of $N$-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe the information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-$N$ limit and the total information-storage capacity increases with $N$ either exponentially or as a power law. The longevity of information-storage also increases with $N$, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with $N$. This connection reveals that the origin of black hole information storage lies in the quantum criticality of the graviton Bose-gas, and that much simpler systems that can be manufactured in table-top experiments can exhibit very similar information-processing dynamics.