Quantum phases of a bosonic generalization of the Moore-Read ansatz

Abstract

I investigate a generalization of the quantum many-body trial wave-function due to Moore and Read (MR). The generalization extends the fermionic MR wave-function to spin-lattices in non-trivial topological phases. These Spin-MR wave-functions are defined as expectation values of local operators in an auxiliary conformal field theory (CFT). The tensor-network formalism naturally discretizes the functional dependence of a Spin-MR wave-function on its auxiliary theory. I derive within the tensor-network formalism original analytical approximations of Spin-MR expectation values. My approximations map expectation values of Spin-MR states to correlation functions of field theories defined in perturbation theory by the Spin-MR auxiliary CFT. Spin-MR states admit a lattice-gas interpretation as multi-component plasmas: interpreted in this way, my approximations are exact in the dilute, large-system-size limit. I consider families of Spin-MR examples in which the perturbed theory is explicitly solvable, allowing me to show the existence of a phase transition between massive and massless Spin-MR states. I apply my analytical method to calculate the entanglement spectra of example Spin-MR states, including confirmation of a result of Scaffidi and Ringel. Entanglement spectra are important diagnostics of symmetry protected topological (SPT) order. I discuss the usefulness of my analytical method as part of a numerical research program to search for non-trivial SPT order in the space of Spin-MR states.