Matrix Quantum Mechanics from Qubits

TL;DR

This paper introduces a nonlocal quantum spin model with large N behavior, revealing a matrix saddle that captures phase transitions and emergent spacetime features at criticality.

Contribution

It presents a novel large N matrix saddle in a nonlocal quantum spin model, connecting quantum phase transitions to emergent spacetime phenomena.

Findings

Large N saddle enhances symmetry to O(N)

Matrix eigenvalue distribution becomes disconnected at transition

Low energy excitations form waves in emergent 1+1D spacetime

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.