Nonreciprocal quantum transport at junctions of structured leads

Eduardo Mascarenhas, François Damanet, Stuart Flannigan, Luca Tagliacozzo, Andrew J. Daley, John Goold, and Inés de Vega

Phys. Rev. B 99, 245134 – Published 19 June 2019

Abstract

We propose and analyze a mechanism for rectification of spin transport through a small junction between two spin baths or leads. For interacting baths, we show that transport is conditioned on the spacial asymmetry of the quantum junction mediating the transport, and attribute this behavior to a gapped spectral structure of the lead-system-lead configuration. For noninteracting leads, a minimal quantum model that allows for spin rectification requires an interface of only two interacting two-level systems. In our paper, we have performed a thorough study of the current, including its time dependence and steady-state value. We obtain approximate results with a weak-coupling Born master equation in excellent agreement with matrix-product-state calculations that are extrapolated in time by mimicking absorbing boundary conditions. These results should be observable in controlled spin systems realized with cold atoms, trapped ions, or in electrons in quantum dot arrays.

Received 18 January 2019
Revised 10 April 2019

DOI:https://doi.org/10.1103/PhysRevB.99.245134

Physics Subject Headings (PhySH)

Quantum transport

1-dimensional spin chains

Quantum master equation Tensor network methods

Condensed Matter, Materials & Applied PhysicsGeneral PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Eduardo Mascarenhas¹, François Damanet¹, Stuart Flannigan¹, Luca Tagliacozzo^1,2, Andrew J. Daley¹, John Goold³, and Inés de Vega⁴

¹Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
²Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
³School of Physics, Trinity College Dublin, The University of Dublin, College Green Dublin 2, Ireland
⁴Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universitat Munchen, D-80333 Munchen, Germany

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Issue

Vol. 99, Iss. 24 — 15 June 2019

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Images

Figure 1
(a) Representation of bath-system-bath coupling and effective evolution of the central interface that depends on its past history and time correlations of the bath. (b) The system-lead state $| Ψ 〉$ depicted as a matrix product state reflecting the corresponding Hamiltonian structure of bulk-coupling. (c) The small asymmetric interface between the leads is represented as a two-qubit structure. (d) The system-bath asymptotic nonequilibrium spectral function $A_{Π} (ω)$ under the Born approximation for different $J_{z}$ couplings showing the spectral structure of the bath with a gap around $ω = 0$ for certain regimes in the limit $H_{S} ≪ H_{B}$ ( $J_{S}, γ = 0.01 J$ ).
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Figure 2
Currents at each bond in one of the leads without (top left) and with (top right) absorbing boundaries for $J_{z} = J$ , $J_{z}^{system} = 0$ and $J_{S} = Δ = γ = 0.01 J$ . Reflection from the boundaries are suppressed in the right panel. Bottom left: The MPS, Kubo, and Born spin currents as a function of time at the Heisenberg point $J = J_{z}^{bath}$ . The dark-dashed line corresponds to Eq. (B1) and the light-dashed line to Eq. (B3). Bottom right: The corresponding asymptotic currents. Parameters are $J_{z}^{system} = 0$ and $J_{S} = Δ = γ = 0.01 J$ .
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Figure 3
Analytical Kubo results for the short time response. Left: The joint spectral function. Upper right: The rectification factor and (lower-right) the diode factor. Parameters are $J_{z} = J$ .
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Figure 4
Asymptotic Born results for the diode factor for (left) a noninteracting system with interacting leads and (right) an interacting-system with noninteracting leads. We set $Δ = J_{S}$ .
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Figure 5
Infinite boundary MPS (IBMPS) results. Spin projection along $z$ axis for the antiferromagnetic spin-1 Heisenberg model of 100 spins (left) after applying a spin creation operator at site 51, ( $σ_{51}^{†}$ ). Spin current at each bond in one of the leads for our open-system model (right). Reflection from the boundaries are delayed but not suppressed.
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Figure 6
MPS results for correlations with a chain of 200 spins in agreement with the analytical results. Darker colors correspond to lower $J_{z}$ while brighter colors correspond to higher $J_{z}$ . The modulus of the correlation in log-log scale for (upper left) $μ ≫ 1$ . The red dashed line is the asymptotic expression in Eq. (C2), respectively. The Bessel function result is indistinguishable from the MPS results. Upper right: The fitted power-law exponent and (lower right) the corresponding phase frequency, assuming $G_{XXZ} \sim e^{i ϕ t} t^{- α}$ . Thus we have confirmation that $α = 1 / 2$ and $ϕ = 4 J_{z}$ .
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