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arXiv:2005.05041 · Physical Review A

Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders

L. Stenzel, Andrew L. C. Hayward, Ulrich Schollwöck, Fabian Heidrich‐Meisner

Published Aug 17, 2020• 6 citations
arXivHTMLPDF

Abstract

The Harper-Hofstadter model for spinful fermions at two-thirds filling is studied using a hybrid-space DMRG approach. Hall conductivity is computed and topological phases, including the appearance of a ferromagnetic ground state between the strongly interacting 1D and 2D models, are identified.
DOI
10.1103/physreva.102.023315

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We study the ground-state phase diagram of the strongly interacting Harper–Hofstadter–Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in y -direction. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogs of fractional quantum Hall phases at fillings ν = 1/2 and 3/2, where the latter is only found thanks to the hopping anisotropy and the quasi-one-dimensional geometry. At integer fillings—where in the full two-dimensional system the ground-state is expected to be gapless—we observe gapped non-degenerate ground-states: at ν = 1 it shows an odd 'fermionic' Hall conductance, while the Hall response at ν = 2 consists of the transverse transport of a single particle–hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation.
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Since the discovery of the quantum Hall effect, the lattice geometry's influence on charged particles in magnetic fields has been the subject of extensive research. Prototypical models such as the non-interacting Harper-Hofstadter model (HHm) exhibit fractionalization of the Bloch bands with non-trivial topology, manifesting in quantum (spin) Hall phases. Ultracold atomic gases with artificial magnetic fields enabled the experimental study of the non-interacting model, while the effect of strong interactions on the band properties remains an open problem. In this work we study the strongly-interacting bosonic Harper-Hofstadter-Mott model (HHMm) using a reciprocal cluster mean-field (RCMF) method. We obtain a rich groundstate phase diagram featuring striped superfluid, supersolid, and symmetry protected topological (SPT) phases. At filling ν=2\nu=2ν=2 (in contrast to fillings ν=1,3\nu=1, 3ν=1,3) the SPT phase has no fermionic counterpart. Incompressible metastable states at fractional filling are also observed. The SPT phases in the HHMm are promising candidates for realizing strongly-correlated topological phases using cold atoms.
In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν ≤ 1 , bounded below by filling factor ν = 1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν = 1 and ν = 3 . The phases near ν = 1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024
We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold-atom experiments. In these experiments, an additional staggered potential and an artificial Rashba-type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi-metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi-metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.