Extended Bose-Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation

TL;DR

This paper investigates the extended Bose-Hubbard model with pair tunneling, revealing spontaneous symmetry breaking, a fragmented condensate quantum ground state, and the emergence of a pair superfluid phase, with implications for understanding nonlinearity in quantum systems.

Contribution

It provides a detailed analysis of the ground state properties and symmetry breaking mechanisms in the extended Bose-Hubbard model with pair tunneling, linking mean field and quantum descriptions.

Findings

Quantum ground state is unique and real, despite mean field degeneracy.

Spontaneous symmetry breaking occurs with infinitesimal perturbations at large particle numbers.

The system exhibits a fragmented condensate with pair correlations.

Abstract

The extended Bose-Hubbard model for a double-well potential with pair tunneling is studied through both exact diagonalization and mean field theory (MFT). When pair tunneling is strong enough, the ground state wavefunction predicted by the MFT is complex and doubly degenerate while the quantum ground state wavefunction is always real and unique. The time reversal symmetry is spontaneously broken when the system transfers from the quantum ground state into one of the mean field ground states upon a small perturbation. As the gap between the lowest two levels decreases exponentially with particle number, the required perturbation inducing the spontaneous symmetry breaking (SSB) is infinitesimal for particle number of typical cold atom systems. The quantum ground state is further analyzed with the Penrose-Onsager criterion, and is found to be a fragmented condensate. The state also develops the pair correlation and has non-vanishing pair order parameter instead of the conventional single particle order parameter. When this model is generalized to optical lattice, a pair superfluid can be generated. The mean field ground state can be regarded as effective ground state in this simple model. The detailed computation for this model enables us to offer an in-depth discussion of the relation between SSB and effective ground state, giving a glimpse on how nonlinearity arises in the SSB of a quantum system.