Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions

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 (SI) transitions. We consider a trimerized Kagomé 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 Rényi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order Rényi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic SI transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic SI transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.

Phase diagram of interacting fermionic two-leg ladder with pair hopping

“…Besides, it should be mentioned that several loophole shape Mott-insulator (LMI) phase regions can also be found in the phase diagram of the single-component bosonic ladder [26] and superlattice [41][42][43][44][45] systems. In the LMI phase, the averaged particle number is a noninteger rather than an integer, which is distinguished from the usual MI phase.…”

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

“…We find that the on-site interaction U and long-range interaction V play an important role on the ground-state phases and the quantum coherence of the special four-chain BH model. In order to show the effects of the long-range interaction on the regular four-chain BH model, we study the quantum phase transition in a regular four-chain BH model by using the cluster Gutzwiller mean-field method [27,28]. Here, the cluster Gutzwiller mean-field method keeps the intrachain tunnelling terms and only decouples the inter-chain tunnelling terms, which is different from the single-site meanfield method.…”

Pairing Superfluid–Insulator Transition Induced by Atom–Molecule Conversion in Bosonic Mixtures in Optical Lattice

“…The entanglement entropy (EE) has been regarded as a typical signature of quantum phase transition in various many-body quantum systems [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. Recently, the secondorder Rényi EE in a bosonic SI transition has also been experimentally measured for ultracold bosonic atoms in optical lattices [56].…”