Cluster Mean-Field Signature of Entanglement Entropy in Bosonic Superfluid-Insulator Transitions

TL;DR

This paper introduces a cluster mean-field approach to analyze entanglement entropy in bosonic superfluid-insulator transitions, revealing entanglement signatures and fractional insulator phases in a trimerized Kagome lattice.

Contribution

It is the first to incorporate entanglement entropy analysis within a cluster mean-field framework for bosonic lattice models.

Findings

Residual bipartite entanglement quantifies phase transitions.

Fractional insulator phases emerge with intra-trimer tunneling dominance.

First-order derivative of Renyi entropy signals phase boundaries.

Abstract

Entanglement entropy (EE), a fundamental conception in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, for the first time, in the framework of a cluster MF treatment, we extract the signature of EE in the bosonic superfluid-insulator transitions. We consider a trimerized Kagome lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all inter-trimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intra-trimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Renyi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order Renyi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic superfluid-insulator transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic superfluid-insulator transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.