基于量子比特的矩阵量子力学
Matrix Quantum Mechanics from Qubits
摘要：
本文引入了一个横场伊辛模型，其中N^2阶自旋通过非定域四次相互作用相互作用。该模型具有O（N，Z）超八面体对称性。我们证明了大N配分函数存在一个鞍点，在鞍点上对称性提高到O（N）。我们进一步证明，这个“矩阵鞍”正确计算大N观测在弱耦合和强耦合。矩阵鞍在中间耦合处经历连续的量子相变。在过渡处，矩阵特征值分布变得不连续。临界激发用大N矩阵量子力学描述。在临界点，低能激发是在1+1维出射时空中传播的波。
英文摘要：
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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