Matrix Quantum Mechanics from Qubits
arXiv:1608.05090 · doi:10.1007/JHEP01(2017)010
Abstract
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
28 pages + Appendices and References. 3 Figures
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- Three Dimensional View of Arbitrary SYK models
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- Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation
- Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
- Correlations vs connectivity in R-charge
- Polynomial solution of quantum Grassmann matrices
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