Topological Frustration can modify the nature of a Quantum Phase Transition

TL;DR

This paper demonstrates that topological frustration, induced by boundary conditions, can fundamentally alter the nature of a second order quantum phase transition in a 1D system, challenging traditional assumptions.

Contribution

It provides the first example showing topological frustration can change the order of a quantum phase transition, highlighting the importance of boundary conditions.

Findings

Topological frustration can eliminate local order parameters.

Boundary conditions can trigger topological frustration in 1D chains.

The nature of the phase transition can be fundamentally altered by topological effects.

Abstract

Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.