Universal Quantum Hamiltonians

Understand

Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena.

• Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models.
• We first characterise precisely what it means for one quantum many-body system to replicate the entire physics of another.
• We then show that certain very simple spin-lattice models are universal in this very strong sense.