Topological Frustration can modify the nature of a Quantum Phase Transition

Vanja Marić,Salvatore Marco Giampaolo,Gianpaolo Torre,Fabio Franchini

doi:10.21468/scipostphys.12.2.075

Vanja Marić, Salvatore Marco Giampaolo + Show 2 more

Open Access

https://doi.org/10.21468/scipostphys.12.2.075

Copy DOI

Journal: SciPost Physics	Publication Date: Feb 24, 2022
Citations: 4	License type: CC BY 4.0

Affiliation: Rudjer Boskovic Institute, University of Zagreb

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.

Highlights

In [18], we have shown that a wide class of topologically frustrated models, to which the 2-cluster-Ising belongs, cannot exhibit a finite local order parameter in the vicinity of the classical antiferromagnetic point (φ = 0), unless the difference between the momenta of two ground states tends to ±π in the thermodynamic limit
We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases
In some cases, Frustrated Boundary Conditions (FBC) generates a topological frustration (TF) that prevents the emergence of any local order, as quantified by observables spreading over a finite support and breaking a Hamiltonian symmetry and the system remains locally disordered across the QPT

Summary

Introduction

In [18], we have shown that a wide class of topologically frustrated models, to which the 2-cluster-Ising belongs, cannot exhibit a finite local order parameter in the vicinity of the classical antiferromagnetic point (φ = 0), unless the difference between the momenta of two ground states tends to ±π in the thermodynamic limit. Since in our case we have that this difference tends to π/2, the expectation values of all local observables that can play the role of order parameter vanish in the thermodynamic limit close to the point φ = 0 and, we expect that they stay equal to zero until the quantum critical point at φ = π/4 is reached.

Results

Conclusion