Speaker
Description
Traditional Hamiltonian lattice gauge theory (LGT) regularizes continuum gauge fields using bosonic link degrees of freedom, leading to infinite-dimensional local Hilbert spaces. Qubit regularization takes a different route: it builds new gauge-invariant quantum lattice systems with finite-dimensional local Hilbert spaces from the outset and obtains continuum relativistic quantum field theories (QFTs) by tuning to quantum critical points. In our work, we do not view these systems as finite-dimensional truncations of an existing LGT. Instead, we regard them as a new class of gauge-invariant lattice gauge theories in their own right and ask whether they possess continuum limits and whether some of the continuum QFTs that emerge in these limits correspond to conventional continuum gauge theories.
As a first application of this research direction, in this talk I will discuss simple qubit-regularized SU(2) and SU(3) LGTs on plaquette chains. Both models give rise to nontrivial, asymptotically safe continuum relativistic QFTs. The SU(2) model maps to the transverse-field Ising model in a longitudinal field, with a continuum limit described by the 2D Ising conformal field theory (CFT) in the ultraviolet (UV) and massive relativistic excitations in the infrared (IR) governed by Zamolodchikov’s $E_8$ QFT. The SU(3) model is equivalent to the three-state quantum clock model in a magnetic field, whose continuum limit is governed by the 2D $\mathbb{Z}_3$ parafermion CFT in the UV and a massive relativistic three-state Potts field theory in the IR. Our lattice models allow us to interpret these traditional continuum QFTs as gauge theories. We have computed universal ratios involving string tensions and the lowest glueball masses, which are standard physical observables in conventional gauge theories. This research points a way toward explorations in higher dimensions.