Universal Translationally-Invariant Hamiltonians

Understand

In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems.

• We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open boundaries, and translational symmetry to simulate any local target Hamiltonian---i.e.
• to reproduce the whole of the target system within its low-energy subspace to arbitrarily-high precision.
• Since this implies the capability to simulate non-translationally-invariant many-body systems with translationally-invariant couplings, any effect such as characteristics commonly associated to systems with external disorder, e.g.