The Frustration of being Odd: Can Boundary Conditions induce a Quantum Phase Transition?

Vanja Marić, Salvatore Marco Giampaolo, Fabio Franchini

Published 2020-02-17Version 1

The answer to the question in the title is clearly ``No'', but we report on something very similar to that, namely a ``Boundary-less Wetting Transitions'' (BWT). We consider the effect of frustrated boundary condition (FBC) on generic local spin-$1/2$ chains in zero field, specifically, we apply periodic boundary conditions on chains with an odd number of sites. In a previous work, we already proved that when only one antiferromagnetic interaction dominates over ferromagnetic ones, in the thermodynamic limit local order (expressed by the spontaneous magnetization) is destroyed. Here, we show that with two competing AFM interactions a new type of order can emerge, with a magnetization profile that varies in space with an incommensurate pattern. This modulation is the result of a ground state degeneracy which leads to a breaking of translational invariance. The transition between the two cases is signaled by an intensive discontinuity in the first derivative of the ground state energy: this is thus not a standard first-order QPT, but rather looks like a boundary QPT, in a system without boundaries, but with FBC.