On universal Hamiltonian simulators

Talk

Spin models are a broad class of models widely used in condensed matter and other complex systems, which exhibit very rich physics, such as different phases, symmetries, and different universality classes. Here we show that there exist `universal hamiltonian simulators' (UHS) whose low energy physics equals the physics of any other classical spin model. This means that the low-energy spectrum is identical to the entire spectrum of any other model, the spin configurations (in a subset of the spins of the UHS) also coincide, and the partition function is the same up to an exponentially small factor. We give sufficient and necessary conditions for a spin model to be a UHS, and find that the 2D Ising model with fields is a UHS. This implies that the low energy physics of the 2D Ising model with fields with tuneable coupling strengths can reproduce all spin physics. The role of UHS for classical simulation is similar to that of universal Turing machines for computation.

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