Ternary unitary quantum lattice models and circuits in 2+1 dimensions

Recently special two-particle gates dubbed dual unitary gates were introduced that admit an interpretation of unitarity in time and space when used in a brick-wall pattern(1). We extended this concept to two spatial dimensions in the form of operators called ternary unitary which are unitary in time and in both spatial dimensions. There are a variety of ways to construct such operators from the lower dimensional dual unitary operators. The most notable feature that arises from the properties of ternary unitary operators is that when used as a time-evolution they admit exact computations of quantities. For example, the dynamical correlation functions exhibit a light-ray structure.     «

Recently special two-particle gates dubbed dual unitary gates were introduced that admit an interpretation of unitarity in time and space when used in a brick-wall pattern(1). We extended this concept to two spatial dimensions in the form of operators called ternary unitary which are unitary in time and in both spatial dimensions. There are a variety of ways to construct such operators from the lower dimensional dual unitary operators. The most notable feature that arises from the properties of...     »