Strong correlations and topological order in one-dimensional systems

Simone Barbarino

V. Yu. Irkhin, Yu. N. Skryabin

K. B. Efetov, A.I. Lapkin

Anna Francuz, Jacek Dziarmaga

The iPEPS tensor network, which is free of the sign problem notorious for the quantum Monte Carlo, is the method of choice to search for topological order in two-dimensional strongly correlated systems. However, finding a ground state represented by iPEPS is one problem, while extracting from this representation the desired information about topological order is quite another. The algorithm, proposed by the authors, does precisely this in a wide class of non-Abelian string net models.

Arianna Montorsi, Utso Bhattacharya, Daniel González-Cuadra +3 more

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such an interacting phase turns out to be revealed by both long-range order of a nonlocal string correlation function and by even degeneracy of the entanglement spectrum. For strong interactions we instead find that the topological crystalline phase is destroyed and replaced by a singlet superconducting phase. The latter, characterized by local fermionic pairing, turns out to appear both in a homogeneous and in a phase separated form. Relevantly, the derived one-dimensional model and the second-order topological insulator can be explored and investigated in atomic quantum simulators.

Fabian Grusdt, Michael H oning, Michael Fleischhauer