Abstract: The 1+1 dimensional gauge theories have served as useful models of quark confinement. I will revisit the classic Schwinger model and its lattice Hamiltonian formulation, where it can be reduced to a model of qubits with long-range interactions. A mass shift between the lattice and continuum definitions of mass, which is motivated by chiral symmetry, is shown to lead to improved results. I will also present the zero-temperature phase diagram of the two-flavor Schwinger model at theta=pi, which exhibits dimensional transmutation and spontaneous breaking of charge conjugation. Finally, I will discuss Adjoint QCD2, which is the 2D SU(N) gauge theory coupled to an adjoint multiplet of Majorana fermions. This model has a rich topological structure. I will introduce a Hamiltonian lattice gauge theory approach to Adjoint QCD2, in which one can compute its low-lying spectrum, the string tensions, and other observables.
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