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Feng L, Katz O, Haack C, Maghrebi M, Gorshkov AV, Gong Z, Cetina M, Monroe C. Continuous symmetry breaking in a trapped-ion spin chain. Nature 2023; 623:713-717. [PMID: 37968402 DOI: 10.1038/s41586-023-06656-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 09/20/2023] [Indexed: 11/17/2023]
Abstract
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.
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Affiliation(s)
- Lei Feng
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Or Katz
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Casey Haack
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Mohammad Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansings, MI, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA
| | - Zhexuan Gong
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Marko Cetina
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Christopher Monroe
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
- IonQ, Inc., College Park, MD, USA.
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2
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Pandey S, Zhang H, Yang J, May AF, Sanchez JJ, Liu Z, Chu JH, Kim JW, Ryan PJ, Zhou H, Liu J. Controllable Emergent Spatial Spin Modulation in Sr_{2}IrO_{4} by In Situ Shear Strain. PHYSICAL REVIEW LETTERS 2022; 129:027203. [PMID: 35867461 DOI: 10.1103/physrevlett.129.027203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 05/16/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that the competition of anisotropic interactions of orthogonal irreducible representations can be a general route to obtain new exotic magnetic states. We demonstrate it here by observing the emergence of a continuously tunable 12-layer spatial spin modulation when distorting the square-lattice planes in the quasi-two-dimensional antiferromagnetic Sr_{2}IrO_{4} under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain-activated anisotropic interaction which is at the fourth order and competing with the inherent quadratic anisotropic interaction. Such a mechanism of competing anisotropy is distinct from that among the ferromagnetic, antiferromagnetic, and/or the Dzyaloshinskii-Moriya interactions, and it could be widely applicable and highly controllable in low-dimensional magnets.
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Affiliation(s)
- Shashi Pandey
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Han Zhang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Junyi Yang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Andrew F May
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Joshua J Sanchez
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Zhaoyu Liu
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Jiun-Haw Chu
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Jong-Woo Kim
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Philip J Ryan
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
- School of Physical Sciences, Dublin City University, Dublin 11, Ireland
| | - Haidong Zhou
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Jian Liu
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
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Lin LF, Zhang Y, Alvarez G, Moreo A, Dagotto E. Origin of Insulating Ferromagnetism in Iron Oxychalcogenide Ce_{2}O_{2}FeSe_{2}. PHYSICAL REVIEW LETTERS 2021; 127:077204. [PMID: 34459630 DOI: 10.1103/physrevlett.127.077204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 07/16/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
An insulating ferromagnetic (FM) phase exists in the quasi-one-dimensional iron oxychalcogenide Ce_{2}O_{2}FeSe_{2}, but its origin is unknown. To understand the FM mechanism, here a systematic investigation of this material is provided, analyzing the competition between ferromagnetic and antiferromagnetic tendencies and the interplay of hoppings, Coulomb interactions, Hund's coupling, and crystal-field splittings. Our intuitive analysis based on second-order perturbation theory shows that large entanglements between doubly occupied and half filled orbitals play a key role in stabilizing the FM order in Ce_{2}O_{2}FeSe_{2}. In addition, via many-body computational techniques applied to a multiorbital Hubbard model, the phase diagram confirms the proposed FM mechanism.
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Affiliation(s)
- Ling-Fang Lin
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Yang Zhang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Gonzalo Alvarez
- Computational Sciences and Engineering Division and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Adriana Moreo
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Elbio Dagotto
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators. Nat Commun 2021; 12:2955. [PMID: 34011947 PMCID: PMC8134496 DOI: 10.1038/s41467-021-23261-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 04/21/2021] [Indexed: 11/08/2022] Open
Abstract
Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.
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