The one-dimensional interacting topological insulator is studied by means of exact diagonalization method. The topological properties are examined with the existence of the edge states and the quantized berry phase at half-filling. It is found that the topological phases are not only robust to small repulsive interactions but also are stabilized by small attractive interactions and also finite repulsive interaction can drive a topological nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.The one-dimensional interacting topological insulator is studied by means of exact diagonalization method. The topological properties are examined with the existence of the edge states and the quantized berry phase at half-filling. It is found that the topological phases are not only robust to small repulsive interactions but also are stabilized by small attractive interactions and also finite repulsive interaction can drive a topological nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.

International Journal of Modern Physics BFeb 7, 20130 citations

Topological phase in a one-dimensional interacting fermion system

Huaiming Guo, Shun-Qing Shen

We study a one-dimensional (1D) interacting topological model by means of the exact diagonalization method. The topological properties are first examined with the existence of the edge states at half-filling. We find that the topological phases are not only robust to small repulsive interactions, but also are stabilized by small attractive interactions, and also finite repulsive interaction can drive a topological nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. Next we calculate the Berry phase and parity of the bulk system and find that they are equivalent in characterizing the topological phases. With them we obtain the critical interaction strengths and construct part of the phase diagram in the parameters' space. Finally we discuss the effective Hamiltonian at the large- $U$ limit and provide an additional understanding of the numerical results. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.We study a one-dimensional (1D) interacting topological model by means of the exact diagonalization method. The topological properties are first examined with the existence of the edge states at half-filling. We find that the topological phases are not only robust to small repulsive interactions, but also are stabilized by small attractive interactions, and also finite repulsive interaction can drive a topological nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. Next we calculate the Berry phase and parity of the bulk system and find that they are equivalent in characterizing the topological phases. With them we obtain the critical interaction strengths and construct part of the phase diagram in the parameters' space. Finally we discuss the effective Hamiltonian at the large-$U$ limit and provide an additional understanding of the numerical results. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.

arXiv:1108.4996Physical Review BNov 4, 201167 citations

Interaction effects and quantum phase transitions in topological insulators

Christopher N. Varney, Kai Sun, Marcos Rigol +1 more

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T=0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T=0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

arXiv:1007.3502Physical Review BSep 28, 2010142 citations

Hard-core bosons in one-dimensional interacting topological bands

Huaiming Guo

We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.

arXiv:1304.3958Physical Review ANov 30, 201212 citations

Phase diagram and topological superfluid state of spin-orbit coupled Fermi gas with attractive interactions in a one-dimensional optical lattice

Haiping Hu, Cheng Chen, Yucheng Wang +2 more

Based on density matrix renormalization group method, we investigate the spin-orbit coupled Fermi gas with attractive interactions in one-dimensional optical lattice and present a complete phase diagram for a quarter-filling system with intermediate strong interactions. We unveil the exotic pairings induced by spin-orbit couplings and the phase transitions between different pairing states, and further demonstrate the existence of the long-sought topological superfluid state at moderate magnetic field and spin-orbit coupling strength. For the particle conserved system, this topological superfluid state can be fixed by its gapless single particle excitation, Luttinger parameter and non-trivial boundary effect. Our study removes out the widespread doubt on the existence of topological superfluid in one dimension and paves the way for simulating topological superfluid states in cold atom settings.Based on density matrix renormalization group method, we investigate the spin-orbit coupled Fermi gas with attractive interactions in one-dimensional optical lattice and present a complete phase diagram for a quarter-filling system with intermediate strong interactions. We unveil the exotic pairings induced by spin-orbit couplings and the phase transitions between different pairing states, and further demonstrate the existence of the long-sought topological superfluid state at moderate magnetic field and spin-orbit coupling strength. For the particle conserved system, this topological superfluid state can be fixed by its gapless single particle excitation, Luttinger parameter and non-trivial boundary effect. Our study removes out the widespread doubt on the existence of topological superfluid in one dimension and paves the way for simulating topological superfluid states in cold atom settings.

arXiv:1511.01762Nov 5, 20150 citations

Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices

Tianhe Li, Huaiming Guo, Shu Chen +1 more

The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $\ensuremath{\pi}$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a $\frac{1}{3}$ -filling topological phase on a background of trivial charge-density-wave or Mott insulators.The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $\ensuremath{\pi}$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a $\frac{1}{3}$-filling topological phase on a background of trivial charge-density-wave or Mott insulators.

arXiv:1502.03876Physical Review BApr 10, 201516 citations

U

limit and provide an additional understanding of the numerical results. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.

T=0

as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

\frac{1}{3}

-filling topological phase on a background of trivial charge-density-wave or Mott insulators.