APS March meeting, Las Vegas, 05-10 March 2023

Abstract

The Frustration of Being Odd

We consider the effects of so-called Frustrated Boundary Conditions (FBC) on quantum spin chains, namely periodic BC with an odd number of sites. In absence of external fields, FBC allow for the direct determination of correlation functions that signal a spontaneous symmetry breaking, such as the spontaneous magnetization. When paired with anti-ferromagnetic interactions, FBC introduce geometrical frustration into the system and the ground state develops properties which differ from those present with other boundary conditions, such as the disappearance of the usual order, possibly replaced by different ones. We argue that FBC introduce a fractionalized excitation that contributes to long-range order in the system, similar to that enjoyed by SPT phases. Our results prove that even the weakest form of geometrical frustration can deeply affect a system’s properties and pave a way for a bottom-up approach to better understand the effects of frustration and their exploitations also for technological purposes.

Complexity of topologically frustrated systems

In my talk, I will present a summary of our main results about the complexity of the ground states of topologically frustrated systems. A topological frustration arises when, in a short-range antiferromagnetic system made of an odd number of spins, periodic boundary conditions are considered. We characterize the increment of the ground state complexity exploiting different approaches as the analysis of the non-stabilizerness (or “magic”) and of the stochastic irreversibility of the entanglement.

Simulating continuous symmetry models with discrete ones

In the past few years it has been demonstrated that the introduction of a frustration of topological origin in one-dimensional spin-1/2 systems can strongly modify their behavior, e.g. by destroying order parameters or by changing the nature of quantum phase transitions. In this work we show that this phenomenon can be exploited for the realization of quantum simulations. In particular, introducing topological frustration in spin chains characterized by a discrete local symmetry, such as a short-range completely anisotropic Heisenberg model or the XY chain, they develop a region in parameter space where their features mimic those of models whose Hamiltonians possess continuous symmetries. This result, together with those of other works in the same field, points towards the conclusion that topologically frustrated systems constitute interesting and efficient platforms for the development of promising quantum technologies.