Various topological Mott insulators and topological bulk charge pumping in strongly-interacting boson system in one-dimensional superlattice

Abstract

In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.Most of the previous studies have focused on the existence of non-trivial topological phases. Some numerical studies by using the density-matrix renormalization group method (DMRG) confirmed the existence of the non-trivial topological phase called topological Mott insulator (TMI) [6,7,9]. TMI is classified by a topological number such as the Chern number and it has a gap in the bulk but a gapless excitation in the (spacial as well as phase diagram) boundaries. A quantum Monte-Carlo simulation was also carried out to detect the topological phase [10]. However, the existence was verified only in a limited parameter regime, and detailed global phase diagrams are still lacking. In particular, strongly-correlated bosonic topological states with high Chern number in the bulk have not been clarified yet in a global parameter regime, nor it is understood well how the competition between the superlattice potential and the on-site repulsion determines the ground state of the system. Also, there is one important question, i.e., how the topological phases in the obtained phase diagrams are related with the topological charge pumping as bulk topological properties.In this paper, we shall study the above problems in the strongly-interacting boson system by using the exact diagonalization [22,23], and show explicitly relation between the equilibrium topological phases and the topological charge pumping in the adiabatic process by following [24]. From the relation, the global phase diagram plays a role of a guide for detecting various topological charge pumping in the experiments.This paper is organized as follows. The target boson model in the 1D optical superlattice is explained in section 2. Section 3 studies the ground states of the system for the hard-core boson limit. We explain the single particle (SP) equation, which is related to the famous Harper equation in 2D ...

Topological charge pumping of bound bosonic pairs

“…This concept was first introduced by Thouless [25] and may be studied by the generalization of the SSH to the Rice-Mele (RM) model [26]. Recently, with the observation of charge pumping in cold-atom experiments [4][5][6][7], the fate of Thouless pumping in interacting systems, such as the interacting fermionic or bosonic RM model, has attracted a great deal of interest [27][28][29][30][31][32][33].…”

Quantum phases and topological properties of interacting fermions in one-dimensional superlattices

“…This implies that the many-body groundstate must remained gapped, such that an adiabatic limit is well- defined. Therefore, there has been great interest in finding insulating quantum phases for both bosonic [36,[39][40][41][42] and fermionic [35,39] systems. Furthermore, one can also establish an analogy to the spin-Quantum Hall effect by studying families of such 1D Hamiltonians with a spin-dependent optical potential [35,39].…”

Simulating bosonic Chern insulators in one-dimensional optical superlattices

“…We find that in the Mott insulator regime, C MB = 1 is independent of U as long as g/h < 1, while C MB = 0 when g/h > 1. This result can be understood for hardcore bosons as a topological (trivial) band insulator with a fully filled lowest single-particle band characterized by nonzero (zero) Chern numbers after mapping to free fermions, and due to the gapped nature of the Mott insulators, the corresponding topological numbers are kept at finite U [80][81][82]. We also check that C MB is independent of the system-size L by calculating C MB from L = 8 to L = 60 using both ED and DMRG, with two examples shown in Fig.…”

“…The bosonic integer quantum Hall state is a U (1) symmetryprotected topological phase [72,73], which could be realized with interacting bosonic atoms in 2D optical lattices under an artificial magnetic field as extended Bosehubbard models [63][64][65]. The topological Mott insulator was first predicted in a 2D honeycomb lattice of interacting fermions [67], and then was shown to be a generic class of interaction-induced topological insulators for interacting fermions or bosons in different dimensions [68][69][70][71][74][75][76][77][78][79][80][81][82][83][84][85][86][87]. Several schemes have been proposed to realize the topological Mott insulating phase by using interacting bosonic or fermionic atoms in 2D optical lattices [74,75] and 1D optical superlattices [80][81][82][83][84][85][86][87].…”