Quantum fluctuations beyond the Gutzwiller approximation in the Bose-Hubbard model

Year: 2020

Authors: Caleffi F., Capone M., Menotti C., Carusotto I., Recati A.

Autors Affiliation: Int Sch Adv Studies SISSA, I-34136 Trieste, Italy; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy; CNR IOM Democritos, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Trento Inst Fundamental Phys & Applicat, I-38123 Trento, Italy.

Abstract: We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of weakly interacting gases. The control parameter of the theory, defined as the zero point fluctuations on top of the Gutzwiller mean-field state, remains small in all regimes. The approach provides accurate results throughout the whole phase diagram, from the weakly to the strongly interacting superfluid and into the Mott insulating phase. As specific examples of application, we study the two-point correlation functions, the superfluid stiffness, and the density fluctuations, for which quantitative agreement with available quantum Monte Carlo data is found. In particular, the two different universality classes of the superfluid-insulator quantum phase transition at integer and noninteger filling are recovered.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 2 (3)      Pages from: 33276-1  to: 33276-11

More Information: The authors thank S. Sachdev for useful discussions. C.M., I.C., and A.R. acknowledge financial support from the Provincia Autonoma di Trento and from the FET-Open Grant MIR-BOSE (No. 737017) and Quantum Flagship Grant PhoQuS (No. 820392) of the European Union. M.C. acknowledges financial support from MIUR PRIN 2015 (Prot. 2015C5SEJJ001) and SISSA/CNR project Superconductivity, Ferroelectricity and Magnetism in bad metals (Prot. 232/2015).
KeyWords: Mott Insulator; Superfluid; Atoms; Metal; Gas
DOI: 10.1103/PhysRevResearch.2.033276

Citations: 14
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