One-way street for the energy current: A ubiquitous phenomenon in boundary-driven quantum spin chains

¹ Departamento de Física–Instituto de Ciências Exatas, Universidade Federal de Minas Gerais CP 702, 30.161-970 Belo Horizonte MG, Brazil
² Departamento de Estatística, Física e Matemática, CAP – Universidade Federal de São João del- Rei 36.420-000, Ouro Branco, MG, Brazil

^(a) emmanuel@fisica.ufmg.br
^(b) humbertolemos@ufsj.edu.br

Received: 13 September 2019
Accepted: 20 January 2020

Abstract

Focusing on the description of nontrivial properties of the energy transport at quantum scale, we investigate asymmetrical quantum spin chains described by boundary-driven and Heisenberg models. We search for symmetries properties of the Lindblad master equation related to the dynamics of the system in order to establish properties of the steady state. Under rather general assumptions for the target polarization at the boundaries, we show the occurrence of an effect related to (but stronger than) energy rectification, namely, the one-way street phenomenon, which is the existence of an unique way for the energy flow. Precisely, the energy current does not change in magnitude and direction as we invert the baths at the boundaries: its direction is completely determined by the asymmetry in the bulk of the chain. The results follow independently of the system size and of the transport regime. Our findings show the ubiquitous occurrence of the one-way street phenomenon for the energy flow in boundary-driven spin systems and, we believe, they shall be an useful contribution to the area devoted to the investigation and building of efficient quantum devices used to control and manipulate the energy current.