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arXiv · 1608.05090

Matrix Quantum Mechanics from Qubits

Sean A. Hartnoll·Liza Huijse·Edward A. Mazenc
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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.

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Sean A. Hartnoll, Liza Huijse, Edward A. Mazenc. 2016-08-17. Matrix Quantum Mechanics from Qubits. https://doi.org/10.1007/jhep01(2017)010

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