Nambu-Goldstone effective theory of information at quantum criticality
EntityUAM. Departamento de Física Teórica
PublisherAmerican Physical Society
10.1103/PhysRevD.92.125002Physical Review D 92.12 (2015): 125002
ISSN1550-7998 (print); 1550-2368 (online)
Funded byThe work of G. D. was supported by the Humboldt Foundation under Alexander von Humboldt Professorship, the ERC Advanced Grant “UV-completion through Bose-Einstein Condensation (Grant No. 339169) and by the DFG cluster of excellence “Origin and Structure of the Universe”, FPA 2009-07908, CPAN (CSD2007- 00042) and HEPHACOSP-ESP00346. The work of C. G. was supported in part by the Humboldt Foundation and by Grants: FPA 2009-07908, CPAN (CSD2007-00042) and by the ERC Advanced Grant 339169 “Selfcompletion.” The work of A. F. was supported by the FCT through the Grant No. SFRH/BD/77473/2011. The work of N. W. was supported by the Swedish Research Council (VR) through the Oskar Klein Centre
ProjectGobierno de España. FPA2009-07908; Gobierno de España. CSD2007- 00042; info:eu-repo/grantAgreement/EC/FP7/339169; Comunidad de Madrid. P-ESP-00346/HEPHACOS
Rights© 2015 American Physical Society
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 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
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