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katayoon razjouyan
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Matrix Quantum Mechanics from Qubits
Angeliki Gazi
et al.
Aug 17, 2016
We introduce a transverse field Ising model with order N^2 spins interactingvia 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 inwhich the symmetry is enhanced to O(N). We further demonstrate that this`matrix saddle' correctly computes large N observables at weak and strongcoupling. The matrix saddle undergoes a continuous quantum phase transition atintermediate couplings. At the transition the matrix eigenvalue distributionbecomes disconnected. The critical excitations are described by large N matrixquantum mechanics. At the critical point, the low energy excitations are wavespropagating in an emergent 1+1 dimensional spacetime.
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