paper

Emergence of helicity +/- 2 modes (gravitons) from qubit models

arXiv:0907.1203 · doi:10.1016/j.nuclphysb.2012.05.010

Abstract

The general equivalence principle and the associated diffeomorphism gauge symmetry are regarded as a founding principles of nature. But, one may wonder, can diffeomorphism gauge symmetry emerge as a low energy property of certain topological/quantum order in a qbit model that has no diffeomorphism gauge symmetry? In this paper, we showed that, at least, the linearized diffeomorphism gauge symmetry h_{μν}\to h_{μν} +\prt_μf_ν+\prt_νf_μcan indeed emerge from some qbit models (or quantum spin models). Physically, the emergence of the (linearized) diffeomorphism gauge symmetry implies the emergence of gapless helicity +/- 2 excitations (ie the gravitons). In the first qbit model (called the L-type model), we show that helicity +/- 2 gapless excitations appear as the only type of low energy excitations using a reliable semiclassical approach. The dispersion of the gapless helicity +/- 2 is found to be \eps_k \propto k^3. The appearance of the gapless helicity +/- 2 modes suggests that the ground state of the qbit model is a new state of matter. In the second model (called the N-type model) the collective modes are strongly interacting and there is no reliable approach to understand its low energy dynamics. Using a spin-wave/quantum-freeze approach (which is shown to reproduce the correct emergent U(1) gauge theory in a quantum rotor model), we argue that the second model may contain helicity +/- 2 gapless excitations as the only type of low energy excitations with a linear dispersion \om \propto k.

25 pages, 7 figures, RevTeX4

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