Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons

Abstract

Topological states of interacting many-body systems are at the focus of current research due to the exotic properties of their elementary excitations. In this paper we suggest a realistic experimental setup for the realization of a simple version of such a phase. We show how delta-interacting bosons hopping on the links of a one-dimensional (1D) ladder can be used to simulate the thin-torus-limit of the two-dimensional (2D) Hofstadter-Hubbard model at one-quarter magnetic flux per plaquette. Bosons can be confined to ladders by optical superlattices, and synthetic magnetic fields can be realized by far off-resonant Raman beams. We show that twisted boundary conditions can be implemented, enabling the realization of a fractionally quantized Thouless pump. Using numerical density-matrix-renormalization-group (DMRG) calculations we show that the groundstate of our model is an incompressible symmetry-protected topological charge density wave (CDW) phase at average filling $\rho =1/8$ per lattice site, related to the 1/2 Laughlin-type state of the corresponding 2D model.

10 pages, 7 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Fractional Quantum Hall Effect in Optical Lattices
• Half-Filled Lowest Landau Level on a Thin Torus
• Interferometric approach to measuring band topology in 2D optical lattices
• One-Dimensional Theory of the Quantum Hall System
• Quantized pumping and phase diagram topology of interacting bosons
• Solvable models for unitary and non-unitary topological phases

Cited by in corpus (19)

• Thouless pumping and topology
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Quantisation and its breakdown in a Hubbard-Thouless pump
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Interactions enable Thouless pumping in a nonsliding lattice
• Pretopological fractional excitations in the two-leg flux ladder
• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Realization of the Non-endpoint Majorana Bound States in an Extended Kitaev Chain
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Absence of disordered Thouless pumps at finite frequency
• Quantum Hall correlations in tilted extended Bose-Hubbard chains