Restricted Boltzmann Machine based on a Fermi sea

In recent years, there has been an intensive research on how to exploit the quantum laws of nature in the machine learning. Models have been put forward which employ spins, photons, and cold atoms. In this work we study the possibility of using the lattice fermions to learn the classical data. We propose an alternative to the quantum Boltzmann Machine, the so-called Spin-Fermion Machine (SFM), in which the spins represent the degrees of freedom of the observable data (to be learned), and the fermions represent the correlations between the data. The coupling is linear in spins and quadratic in fermions. The fermions are allowed to tunnel between the lattice sites. The training of SFM can be eciently implemented since there are closed expressions for the log- likelihood gradient. We nd that SFM is more powerful than the classical Restricted Boltzmann Machine (RBM) with the same number of physical degrees of freedom. The reason is that SFM has additional freedom due to the rotation of the Fermi sea. We show examples for several data sets.

The Planar Thirring Model with Kähler-Dirac Fermions

Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed.

Flavour-selective localization in interacting lattice fermions via SU(N) symmetry breaking

A large repulsion between particles in a quantum system can lead to their localization, as it happens for the electrons in Mott insulating materials. This paradigm has recently branched out into a new quantum state, the orbital-selective Mott insulator, where electrons in some orbitals are predicted to localize, while others remain itinerant. We provide a direct experimental realization of this phenomenon, that we extend to a more general flavour-selective localization. By using an atom-based quantum simulator, we engineer SU(3) Fermi-Hubbard models breaking their symmetry via a tunable coupling between flavours, observing an enhancement of localization and the emergence of flavour-dependent correlations. Our realization of flavour-selective Mott physics opens the path to the quantum simulation of multicomponent materials, from superconductors to topological insulators