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arXiv:1702.00642 · Science

Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators

Timon Hilker, Guillaume Salomon, Fabian Grusdt, Ahmed Omran, Martin Boll, Eugene Demler, Immanuel Bloch, Christian Groß

Published Aug 3, 2017• 215 citations
arXivHTMLPDF

Abstract

Topological phases, like the Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, nonlocal string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems owing to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of nonlocal spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique, which measures nonlocal order directly, can be readily extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.

DOI
10.1126/science.aam8990

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Topological phases, like the Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, nonlocal string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems owing to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of nonlocal spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique, which measures nonlocal order directly, can be readily extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.
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Ultracold neutral atoms in optical lattices have become a powerful platform for the simulation of complex quantum systems. With our quantum gas microscope, we measure snapshots of the quantum many-body wavefunction by fully resolving the position and spin of each atom. I will present the application of this method to two quantum phases: The Haldane spin-1 phase is the prototype of a symmetry-protected topological phase, whose spin order is hidden in conventional two-point correlation functions. On our images, we can evaluate the characteristic string-correlator of this state and directly see the associated edge states of the system. In an antiferromagnetic background, holes get dressed by a surrounding cloud of ferromagnetic correlations. We study these magnetic polarons, which are a building block of the intricate physics of cuprates, by mapping out the spatial structure of the spin environment of individual holes. Upon increased doping, we observe the transition from this unusual polaronic metal to a Fermi Liquid and provide quantum-simulated results of the Fermi-Hubbard model as a benchmark for different theoretical approaches.
The experimental realization of time-dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one-dimensional two-components lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of hidden magnetic phases, with degenerate protected edge modes. The magnetism, characterized solely by string-like nonlocal order parameters, manifests in the charge and/or in the spin degrees of freedom. Such behavior is enlighten by employing Luttinger liquid theory and numerical methods. The range of parameters for which hidden magnetism is present can be reached by means of the currently available experimental setups and probes.
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Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the two-dimensional Fermi-Hubbard model and effects of doping with holes away from half filling. In this work we show how direct measurements of the system averaged two-spin density matrix and its full counting statistics can be used to identify different correlated magnetic phases with or without long-range order. We discuss examples of phases which are potentially realized in the Hubbard model close to half filling, including antiferromagnetically ordered insulators and metals, as well as insulating spin liquids and metals with topological order. For these candidate states we predict the doping- and temperature dependence of local correlators, which can be directly measured in current experiments.
The experimental realization of time-dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one-dimensional two-components lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of hidden magnetic phases, with degenerate protected edge modes. The magnetism, characterized solely by string-like nonlocal order parameters, manifests in the charge and/or in the spin degrees of freedom. Such behavior is enlighten by employing Luttinger liquid theory and numerical methods. The range of parameters for which hidden magnetism is present can be reached by means of the currently available experimental setups and probes.