Direct Probing of the Mott Crossover in the SU(N) Fermi-Hubbard Model

Abstract

We report on a detailed experimental investigation of the equation of state (EoS) of the three-dimensional Fermi-Hubbard model (FHM) in its generalized SU(N) -symmetric form, using a degenerate ytterbium gas in an optical lattice. In its more common spin-1/2 form, the FHM is a central model of condensed-matter physics. The generalization to N>2 was first used to describe multi-orbital materials and is expected to exhibit novel many-body phases in a complex phase diagram. By realizing and locally probing the SU(N) FHM with ultracold atoms, we obtain model-free access to thermodynamic quantities. The measurement of the EoS and the local compressibility allows us to characterize the crossover from a compressible metal to an incompressible Mott insulator. We reach specific entropies above Néel order but below that of uncorrelated spins. Having access to the EoS of such a system represents an important step towards probing predicted novel SU(N) phases.

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Plain Language Summary

Understanding the physics of strongly interacting materials is critical in condensed matter physics and may lead to new quantum technologies. In particular, fermionic many-body systems, such as the electrons in crystals, are still associated with many unanswered questions. The origin of high-temperature superconductivity, for example, is still unknown. Many of these systems can be described by a so-called Fermi Hubbard model (FHM) and exhibit properties that are notoriously hard to calculate. Here, we experimentally realize a FHM with enhanced spin symmetry and study its thermodynamic properties, shedding light on the behavior of certain fermionic many-body systems.

We focus on an ensemble of ultracold Yb173 atoms in their ground state situated in an optical lattice. This experimental setup allows us to realize a FHM, which was originally developed to explain interacting electrons that possess two spin components with an SU(2) symmetry. By varying the interaction strength between the atoms, we observe the transition from a conducting behavior to that of an insulator. We study the properties of this transition by both globally measuring the total entropy of the system and by locally probing inside the lattice. The details of this transition are dependent on the symmetry of the FHM, which in our system can be extended to the general SU(N) symmetric case. We are accordingly able to directly characterize the transition for different symmetry cases using density and compressibility as observables.

We expect that our findings will be important for advancing knowledge about SU(N) Fermi Hubbard physics and motivating additional studies of SU(N) magnetism.