Density Matrix Renormalization Group Analysis of Quantum Spin Ice

One of the most studied systems in three dimensional many-body physics is a model of spins on the pyrochlore lattice dubbed quantum spin ice. The massive frustration of the model makes it a strong candidate for supporting a variety of exotic spin liquids with natural connections to lattice gauge theory. Here we initiate the use of the Density Matrix Renormalization Group (DMRG) to study the phase diagram of quantum spin ice, focusing on the transition from an XY antiferromagnet to a U(1) spin liquid. Using quasi-one-dimensional cylindrical cuts of the lattice, we compute the local spin properties of the phases and find that they converge remarkably quickly. With more effort, we extract the entanglement entropies and fit them to the Cardy-Calabrese scaling form to extract the central charge. Further discussions on detecting the photon of the U(1) spin liquid and more controversial aspects of the phase diagram may be included.