Topological transitions of interacting bosons in one-dimensional bichromatic optical lattices (original) (raw)
Related papers
Topological insulator of ultra cold atoms in bichromatic optical lattices
We investigate the effect of a strong bichromatic deformation to the mathbbZ2\mathbb{Z}_{2}mathbbZ2 topological insulator in ultracold atomic system proposed by B. B\'eri and N. R. Cooper, Phys.Rev.Lett. 107, 145301 (2011). Large insulating gap of this system allows for examination of strong perturbations. We conclude that the mathbbZ2\mathbb{Z}_{2}mathbbZ2 topological character of the system is robust against a large global perturbation which breaks the inversion symmetry but preserves the time-reversal symmetry.
Topological Properties of 1D Quasicrystal Bose–Mott Insulators
Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013), 2014
Recently, the relation between one-dimensional (1D) quasicrystals and 2D topological insulators has been demonstrated theoretically and also experimentally by using optical waveguides. It has been shown that 1D quasicrystals can be classified in terms of topology for 2D integer quantum Hall systems. Such quasicrystals can be also realized in ultracold atoms loaded in optical superlattices. In this study, we consider a 1D Bose-Hubbard model in a quasiperiodic superlattice. It is known that a gap in the excitation spectrum is induced by the interaction, and the resulting Mott insulating phase is characterized by a nonzero Chern number. The system is called a topological Mott insulator. In the non-interacting case, topological equivalence between the Fibonacci quasicrystal and the Harper model is already known. However, it has not been clarified whether such topological equivalence exists in topological Mott insulators. We show numerically that the topological equivalence exists in a wide range of quasiperiodic Bose-Hubbard model.
Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
Journal of the Physical Society of Japan
We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gapclosing behavior as the interaction strength U is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of U and a continuous deformation parameter β between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.
Topological states in two-dimensional optical lattices
Physical Review A, 2010
We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multi-orbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.
Interaction effects and quantum phase transitions in topological insulators
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.
Topological insulators and metals in atomic optical lattices
Physical Review A, 2009
We propose the realization of topological quantum states with cold atoms trapped in an optical lattice. We discuss an experimental setup that generates a two-dimensional hexagonal lattice in the presence of a light-induced periodic vector potential, which represents a realization of the Haldane model with cold atoms. We determine theoretically the conditions necessary for observing the topological states and show that two of the key conditions are: 1) the realization of sharp boundaries and 2) the minimization of any smoothly varying component of the confining potential. We argue that, unlike their condensed matter counterparts, cold atom topological quantum states can be i) "seen", by mapping out the characteristic chiral edge states, and ii) controlled, by controlling the periodic vector potential and the properties of the confining potential. arXiv:0901.3921v1 [cond-mat.mes-hall]
Microscopic Realization of Two-Dimensional Bosonic Topological Insulators
Physical Review Letters, 2014
It is well known that a Bosonic Mott insulator can be realized by condensing vortices of a boson condensate. Usually, a vortex becomes an anti-vortex (and vice-versa) under time reversal symmetry, and the condensation of vortices results in a trivial Mott insulator. However, if each vortex/anti-vortex interacts with a spin trapped at its core, the time reversal transformation of the composite vortex operator will contain an extra minus sign. It turns out that such a composite vortex condensed state is a bosonic topological insulator (BTI) with gapless boundary excitations protected by U (1) Z T 2 symmetry. We point out that in BTI, an external π flux monodromy defect carries a Kramers doublet. We propose lattice model Hamiltonians to realize the BTI phase, which might be implemented in cold atom systems or spin-1 solid state systems.
Physical Review Letters, 2015
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large offsite interactions on top of a small onsite interaction. Here we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in A and B sublattices makes the onsite interaction Pauli-forbidden, while a sizeable inter-site interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt the density functional theory for cold-atoms, here extended to accommodate non-collinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.
Topological Varma Superfluid in Optical Lattices
Physical Review Letters, 2016
Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a tenfold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.
Scientific Reports
We theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.