A new rung on the ladder: exploring topological frustration towards two dimensions

Abstract: Topological frustration arises when boundary conditions impose geometric frustration in a quantum system, creating delocalized defects in the ground states and profoundly altering the low-energy properties. While previous studies have been concerned with one-dimensional systems, showing that the ground state structure can be described in terms of quasiparticle excitations, the two-dimensional setting remains unexplored. We address this gap by studying a three-legged antiferromagnetic quantum Ising ladder on a torus using tensor network methods, where topological frustration is induced by an odd number of spins along both spatial directions. Our results reveal the first instance in which topological frustration shifts the position of the quantum critical point. By studying the entanglement structure, we find that the ground state can be characterized as hosting three delocalized quasiparticles. This work builds the quasiparticle picture of topological frustration toward higher dimensions and more complex systems than those considered so far.