Abstract
Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.
Highlights
Chiu, Christie, Geoffrey Ji, Annabelle Bohrdt, Muqing Xu, Michael Knap, Eugene Demler, Fabian Grusdt, Markus Greiner, and Daniel Greif. 2019
Upon doping a cold-atom antiferromagnet we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables
An intriguing consequence of the superposition principle is the existence of hidden order in correlated quantum systems: every individual configuration is characterized by a particular pattern, the average over these configurations leads to an apparent loss of order
Summary
The string-pattern-based observables introduced here complement established observables such as correlation functions or full counting statistics. Machine learning techniques could be used to directly compare sets of raw experimental atom distributions to theoretical models without the need for intermediate observables [39] This class of techniques is highly promising as quantum simulations of the Hubbard model continue to probe lower temperatures within the pseudogap and strangemetal phases, but can be applied to spatially resolved studies of quenches across phase transitions [40], dynamical phase transitions [41], and higher-order scattering processes [42]. F. Parsons et al, Physical Review Letters 114, 213002 (2015). Hofstetter, Physical Review Letters 92, 170403 (2004). Data for “String Patterns in the doped Hubbard model.” Harvard Dataverse (2019)
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