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Exploring Interacting Topological Insulators with Ultracold Atoms: The Synthetic Creutz-Hubbard Model

J. Jünemann1,2, A. Piga3, S.-J. Ran3, M. Lewenstein3,4, M. Rizzi1, and A. Bermudez5

  • 1Johannes Gutenberg-Universität, Institut für Physik, Staudingerweg 7, 55099 Mainz, Germany
  • 2MAINZ–Graduate School Materials Science in Mainz, Staudingerweg 9, 55099 Mainz, Germany
  • 3ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
  • 4ICREA, Lluis Companys 23, 08010 Barcelona, Spain
  • 5Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom and Instituto de Física Fundamental, IFF-CSIC, Madrid E-28006, Spain

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Phys. Rev. X 7, 031057 – Published 27 September, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031057

Abstract

Understanding the robustness of topological phases of matter in the presence of strong interactions and synthesizing novel strongly correlated topological materials lie among the most important and difficult challenges of modern theoretical and experimental physics. In this work, we present a complete theoretical analysis of the synthetic Creutz-Hubbard ladder, which is a paradigmatic model that provides a neat playground to address these challenges. We give special attention to the competition of correlated topological phases and orbital quantum magnetism in the regime of strong interactions. These results are, furthermore, confirmed and extended by extensive numerical simulations. Moreover, we propose how to experimentally realize this model in a synthetic ladder made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. Our work paves the way towards quantum simulators of interacting topological insulators with cold atoms.

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Popular Summary

Topological phases of matter and topological phase transitions are a hot topic, as shown by the 2016 Nobel Prize in Physics. The award recognized how the mathematical field of topology, which studies intrinsic properties of shapes, can elucidate strange behaviors seen in certain exotic materials. One of the most difficult and important challenges in this field is to understand how topological insulators and superconductors, whose surfaces have different electrical behavior than their interiors, behave in the presence of strong interactions and correlations among the particles. Since these effects are absent in the majority of topological materials explored so far, synthetic quantum matter engineered in systems of ultracold atoms appears to be a promising platform for testing our understanding. Using theoretical analysis and numerical simulations, we present a way of implementing such a test bed.

We study the imbalanced Creutz-Hubbard ladder, a variant of a type of one-dimensional topological insulator, which provides a simple and paradigmatic playground for exploring these challenges. We present a complete theoretical analysis of the model in all parameter regimes, paying special attention to the robustness of topological features (like edge states) versus more-standard quantum magnetic orderings. Moreover, we present a detailed proposal to realize this model using ultracold fermionic atoms in a one-dimensional optical lattice.

We believe that our work will pave the way toward the quantum simulation of interacting topological insulators with cold atoms and advance the current understanding of correlated topological phases of matter.

Article Text

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Phys. Rev. X 7, 031057– Published 27 September, 2017
  • Received 21 December 2016
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