Quantum phase transitions in the dimerized extended Bose-Hubbard model

Abstract

We present an unbiased numerical density-matrix renormalization group study of the onedimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetryprotected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that the phase boundaries of the Haldane phase to Mott insulator and density-wave states belong to the Gaussian and Ising universality classes with central charges c = 1 and c = 1/2, respectively, and merge in a tricritical point. Interestingly we can demonstrate a direct Ising quantum phase transition between the dimerized Mott and density-wave phases above the tricritical point. The corresponding transition line terminates at a critical end point that belongs to the universality class of the dilute Ising model with c = 7/10. At even stronger Coulomb interactions the transition becomes first order.

Quantum criticality in dimerised anisotropic spin-1 chains

“…We note that a similar situation evolves in the onedimensional extended Bose-Hubbard model with bond dimerisation [16].…”

Quantum criticality in dimerised anisotropic spin-1 chains

“…The calculated ground-state phase diagram shows that a symmetry-protected topological Haldane phase appears-in between large-D and antiferromagnetic phases-for not too large bond dimerisation only. We note that a similar situation evolves in the one-dimensional extended Bose-Hubbard model with bond dimerisation [16].…”

Anomalous bulk-boundary correspondence of topological magnon excitations in a spin chain

“…For a large ∆, all spins downward | ↓↓ • • • ↓ is a ferromagnetic ground state, in which flipping a spin upward creates a magnon excitation. In contrast to the studies of topological ground states [42][43][44][45][46][47][48], topological magnon excitations are associated with ex-cited states. Because the system (1) conserves the total z-direction magnetization, the subspaces with different magnon numbers are decoupled.…”