D-theory provides an alternative lattice regularization of the (1 + 1)-d CP (N − 1) quantum field theory. In this formulation the continuous classical CP (N − 1) fields emerge from the dimensional reduction of discrete SU (N ) quantum spins. In analogy to Haldane's conjecture, ladders consisting of an even number of transversely coupled spin chains lead to a CP (N − 1) model with vacuum angle θ = 0, while an odd number of chains yields θ = π. In contrast to Wilson's formulation of lattice field theory, in D-theory no sign problem arises at θ = π, and an efficient cluster algorithm is used to investigate the θ-vacuum effects. At θ = π there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP (N − 1) models with N > 2.PACS numbers: 05.50.+q,75.10.Jm CP (N − 1) models are interesting (1 + 1)-d quantum field theories [1] which share a number of important features with (3 + 1)-d QCD. These include asymptotic freedom, the dynamical generation of a mass-gap, and an instanton topological charge leading to non-trivial θ-vacuum effects. Despite the fact that Nature has chosen θ = 0, it is an interesting challenge to understand the structure of θ-vacua, which in QCD may, for example, lead to 't Hooft's oblique confinement phases [2]. It has been conjectured that CP (N − 1) models have a phase transition at θ = π. In the CP (1) = O(3) case this phase transition is known to be second order with a vanishing mass-gap [3][4][5]. For N > 2, on the other hand, the transition is conjectured to be first order [6], which is consistent with large N analytic results [7]. For finite N , however, the investigation of these nonperturbative problems is highly nontrivial. In particular, in contrast to O(N ) models and other (1 + 1)-d quantum field theories, CP (N − 1) models with N > 2 cannot be solved with the Bethe ansatz. This is because in the CP (N − 1) case an infinite set of classical symmetries is anomalous and can thus not be used to solve the quantum theory analytically.The numerical investigation of lattice CP (N −1) models is also far from being straightforward, even at θ = 0. Again, in contrast to O(N ) models which can be studied with the efficient Wolff cluster algorithm [8], no efficient cluster algorithm is available for CP (N − 1) models [9]. There is even a no-go theorem that forbids the construction of an efficient Wolff-type embedding algorithm for these models [10]. Still, at θ = 0 a rather efficient multigrid algorithm was developed in [11]. However, at θ = π the situation is much worse due to a very severe sign problem: the contributions from odd topological charge sectors almost completely cancel those from even charge sectors. This makes it exponentially hard to access large lattices which is necessary for reaching reliable conclusions about the phase structure. For this reason, previous numerical studies of θ-vacua were limited to mod- erate volumes [12,13] or rely on additional assumptions [14]. In the CP (1) = O(3) case, a Wolff-type meroncluster algorithm allows...