Towards a phase diagram of the topologically frustrated XY chain

TL;DR

This paper investigates how topological frustration alters the zero-temperature phase diagram of the XY chain in a transverse magnetic field, revealing new quantum phase transitions and a novel second order boundary transition with quartic dispersion.

Contribution

It demonstrates that topological frustration induces new quantum phase transitions in the XY chain, including the first known second order boundary transition with quartic dispersion.

Findings

Topological frustration modifies the phase diagram of the XY chain.

Discovery of a second order boundary quantum phase transition with quartic dispersion.

Analytical and numerical results support the new phase transition insights.

Abstract

Landau theory's implicit assumption that microscopic details cannot affect the system's phases has been challenged only recently in systems such as antiferromagnetic quantum spin chains with periodic boundary conditions, where topological frustration can be induced. In this work, we show that the latter modifies the zero temperature phase diagram of the XY chain in a transverse magnetic field by inducing new quantum phase transitions. In doing so, we come across the first case of second order boundary quantum phase transition characterized by a quartic dispersion relation. Our analytical results are supported by numerical investigations and lay the foundation for understanding the phase diagram of this frustrated model.