On the boundary-driven Heisenberg chain

We study the spin transport in the quantum Heisenberg spin chain subject to boundary magnetic fields and driven out of equilibrium by Lindblad dissipators. An exact solution is given in terms of matrix product states, which allows us to calculate exactly the spin current for any chain size. It is found that the system undergoes a discontinuous spin-valve-like quantum phase transition from ballistic to subdiffusive spin current, depending on the value of the boundary fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate operating with the boundary fields as the base element.We study the spin transport in the quantum Heisenberg spin chain subject to boundary magnetic fields and driven out of equilibrium by Lindblad dissipators. An exact solution is given in terms of matrix product states, which allows us to calculate exactly the spin current for any chain size. It is found that the system undergoes a discontinuous spin-valve-like quantum phase transition from ballistic to subdiffusive spin current, depending on the value of the boundary fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate operating with the boundary fields as the base element.

arXiv:1501.07732Physical Review BMay 20, 201532 citations

Integrability of Heisenberg Chain

Frontiers of research with the Chinese academy of sciencesFeb 1, 20080 citations

Application of Operator Algebras to Stochastic Dynamics and the Heisenberg Chain

Robin B. Stinchcombe, Gunter Markus Schutz

Algebraic manipulations are used to reduce a new description of stochastic dynamics and quantum spin chains involving two nonlocal operators $C,D$ . For the symmetric hopping of hard-core particles, and its associated Heisenberg chain, the operator algebra may be written in the reduced form $2\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}[[C,D]{,C}^{\ensuremath{-}1}]$, ${2D}^{2}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}CDC}^{\ensuremath{-}1}{D+DC}^{\ensuremath{-}1}\mathrm{DC}$. These equations are shown to describe diffusive dynamics and phase change on interchange, respectively, and to lead to Bethe ansatz equations for the spectrum of the isotropic Heisenberg chain with symmetry-breaking boundary fields. This yields new exact results for the dynamics of boundary-driven systems.Algebraic manipulations are used to reduce a new description of stochastic dynamics and quantum spin chains involving two nonlocal operators $C,D$. For the symmetric hopping of hard-core particles, and its associated Heisenberg chain, the operator algebra may be written in the reduced form $2\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}[[C,D]{,C}^{\ensuremath{-}1}]$, ${2D}^{2}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}CDC}^{\ensuremath{-}1}{D+DC}^{\ensuremath{-}1}\mathrm{DC}$. These equations are shown to describe diffusive dynamics and phase change on interchange, respectively, and to lead to Bethe ansatz equations for the spectrum of the isotropic Heisenberg chain with symmetry-breaking boundary fields. This yields new exact results for the dynamics of boundary-driven systems.

Physical Review LettersJul 3, 1995100 citations

The Heisenberg Spin Chain

Carlo Heissenberg, Augusto Sagnotti

Cambridge University Press eBooksJan 6, 20220 citations

Exact Matrix Product Solution for the Boundary-Driven Lindblad XXZ Chain

Dragi Karevski, Vladislav Popkov, Gunter Markus Schutz

We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)[SU(2)]. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)[SU(2)]. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.

arXiv:1211.7010Physical Review LettersJan 24, 2013162 citations

Algebraic manipulations are used to reduce a new description of stochastic dynamics and quantum spin chains involving two nonlocal operators

C,D

. For the symmetric hopping of hard-core particles, and its associated Heisenberg chain, the operator algebra may be written in the reduced form $2\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}[[C,D]{,C}^{\ensuremath{-}1}]$, ${2D}^{2}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}CDC}^{\ensuremath{-}1}{D+DC}^{\ensuremath{-}1}\mathrm{DC}$. These equations are shown to describe diffusive dynamics and phase change on interchange, respectively, and to lead to Bethe ansatz equations for the spectrum of the isotropic Heisenberg chain with symmetry-breaking boundary fields. This yields new exact results for the dynamics of boundary-driven systems.