Probing spontaneously symmetry-broken phases with spin-charge separation through noise correlation measurements

Abstract

Spontaneously symmetry-broken (SSB) phases are locally ordered states of matter characterizing a large variety of physical systems. Because of their specific ordering, their presence is usually witnessed by means of local order parameters. Here, we propose an alternative approach based on statistical correlations of noise after the ballistic expansion of an atomic cloud. We indeed demonstrate that probing such noise correlators allows one to discriminate among different SSB phases characterized by spin-charge separation. As a particular example, we test our prediction on a 1D extended Fermi-Hubbard model, where the competition between local and nonlocal couplings gives rise to three different SSB phases: a charge density wave, a bond-ordering wave, and an antiferromagnet. Our numerical analysis shows that this approach can accurately capture the presence of these different SSB phases, thus representing an alternative and powerful strategy to characterize strongly interacting quantum matter.

We thank T. Esslinger for useful discussions. The numerical calculations were performed using the TenPy Library [55]. K.G.-L. acknowledges the Catalonia Quantum Academy (CQA). The ICFO group acknowledges support from ERC AdG NOQIA; MICIN/AEI (PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI); MICIIN with funding from European Union NextGeneration EU (PRTR-C17.I1): QUANTERA MAQS PCI2019-111828-2; MCIN/AEI/10.13039/501100011033 and by the European UnionNextGeneration EU/PRTRQUANTERADYNAMITE PCI2022-132919 within the QuantERA II Programme that has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 101017733 Proyectos de I+D+I Retos Colaboración QUSPIN RTC2019-007196-7; Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020); Barcelona Supercomputing Center MareNostrum (FI-2023-1-0013); EU (PASQuanS2.1, 101113690); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No. 899794); EU Horizon Europe Program (Grant Agreement No. 101080086–NeQST); National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314); ICFO Internal QuantumGaudi project; European Union’s Horizon 2020 research and innovation program under the Marie-Skłodowska-Curie Grant Agreements No. 101029393 (STREDCH) and No. 847648 (La Caixa Junior Leaders fellowships ID100010434: LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013). C.W. acknowledges funding by the Cluster of Excellence “CUI: Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG)EXC2056-Project ID No. 390715994, by the DFG Research Unit FOR 2414, Project No. 277974659, and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 802701. L.B. acknowledges financial support within the DiQut Grant No.2022523NA7fundedbyEuropean Union NextGeneration EU, PRIN 2022 program (D.D. 10402/02/2022 Ministero dell’Universitá e della Ricerca). J.A.-L. acknowledges support by the Spanish Ministerio de Ciencia e Innovación (MCIN/AEI/10.13039/501100011033, Grant No. PID2023-147469NB-C21), and by the Generalitat de Catalunya (Grant No. 2021 SGR 01411).

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