SP Seminar @SISSA Via Bonomea Room 004 Tuesday 6 November at 11am - Fabio FRANCHINI

[CM Section]

Joint ICTP/SISSA Statistical Physics Seminar

Tuesday 6 November 11:00 a.m.
SISSA, Via Bonomea 265, Room 004

Fabio FRANCHINI (Ruder Boskovic Institute, Zagreb, Croatia)

Title:The Frustration in Being Odd: Area Law Violation in Local Systems

We demonstrate the existence of a new quantum phase of matter that 
arises in antiferromagnetic spin chains with a weak frustration -just 
one bond in a large chain-. This is the case, for instance, of systems 
with an odd number of spins with periodic boundary conditions. Such new 
phase is extended, gapless, but not relativistic: the low-energy 
excitations have a quadratic (Galilean) spectrum. Locally, the 
correlation functions on the ground state do not show significant 
deviations compared to the non-frustrated case, but correlators 
involving a number of sites (or distances) scaling like the system size 
display new behaviors. In particular, the von Neumann entanglement 
entropy is found to follow new rules, for which neither area law 
applies, nor one has a divergence of the entropy with the system size. 
Such very long-range correlations are novel and of potential 
technological interest. We display such new phase in a few prototypical 
chains using numerical simulations and we study analytically the 
paradigmatic example of the Ising chain. Through these examples we argue 
that this phase emerges generally in (weakly) frustrated systems with 
discrete symmetries.

Reference: Salvatore Marco Giampaolo, Flávia Braga Ramos, Fabio 
Franchini: arXiv:1807.07055