The Frustration of being Odd: How Boundary Conditions can destroy Local Order

Marić, Vanja; Giampaolo, Salvatore Marco; Kuić, Domagoj; Franchini, Fabio (2019) The Frustration of being Odd: How Boundary Conditions can destroy Local Order. New Journal of Physics, 22 . ISSN 1367-2630

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Official URL: https://iopscience.iop.org/article/10.1088/1367-26...

Abstract

A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. In this work, we show striking, yet puzzling, evidence of a clear violation of this assumption. We use the prototypical example of an XYZ chain with no external field in a ring geometry with an odd number of sites and both ferromagnetic and antiferromagnetic interactions. In such a setting, even at finite sizes, we are able to calculate directly the spontaneous magnetizations that are traditionally used as order parameters to characterize the system's phases. When ferromagnetic interactions dominate, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with standard expectations. On the contrary, when the system is governed by antiferromagnetic interactions, the magnetizations decay algebraically to zero with the system size and are not staggered, despite the AFM coupling. We term this behavior ferromagnetic mesoscopic magnetization. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one-- spin expectation values on the boundary conditions, which is in contrast with predictions from the general theory.

Item Type:

Article

Uncontrolled Keywords:

Order Parameter ; Frustration ; boundary conditions ; spin chain

Subjects:

NATURAL SCIENCES > Physics

Divisions:

Theoretical Physics Division

Projects:

Project title	Project leader	Project code	Project type
Novel Characterizations of Classical and Quantum Many-Body Systems-ManyBodyCharacteriza	Fabio Franchini	IP-2016-06-3347	HRZZ
Sinergijom do uspjeha: RBI-T-WINNING i ESIF udruženi u jačanju izvrsnosti Zavoda za teorijsku fiziku Instituta Ruđer Bošković-RBI-TWINN-SIN	Blaženka Melić	KK.01.1.1.06.0006	EK
Provedba vrhunskih istraživanja u sklopu Znanstvenog centra izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri-QuantiXLie	Hrvoje Buljan; Pavle Pandžić	KK.01.1.1.01.0004	EK