|
This article is cited in 2 scientific papers (total in 2 papers)
Exact results for the isotropic spin-$1/2$ Heisenberg chain with dissipative boundary driving
V. Popkovab, D. Karevskic, G. M. Schützcd a Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
b Institute of Theoretical Physics, University of Cologne, Cologne, Germany
c Laboratoire de Physique et Chimie Théoriques, Université de Lorraine, CNRS, Vandoeuvre les Nancy, France
d Institute of Complex Systems,
Forschungszentrum Jülich, Germany
Abstract:
We consider the open isotropic spin-$1/2$ Heisenberg quantum spin chain with a finite number $N$ of sites coupled at the ends to a dissipative environment that favors polarization of the boundary spins in different directions. We review the matrix product ansatz (MPA) that yields the exact reduced density matrix of the Heisenberg chain. We develop the matrix algebra coming from the MPA in more detail than in previous work. We hence obtain exact results for the nonequilibrium partition function, about the impact of quantum fluctuations on the targeted boundary states, and for current–magnetization correlations in the steady state. The boundary states turn out to be pure to the order $o(N^{-2})$. We show that the local magnetization and the local current perpendicular to the plane spanned by the boundary polarizations exhibit long-range correlations while the local magnetization correlations with the local in-plane currents are strongly suppressed.
Keywords:
nonequilibrium steady state, Heisenberg spin chain, driven system, exact result.
Received: 20.02.2018 Revised: 20.02.2018
Citation:
V. Popkov, D. Karevski, G. M. Schütz, “Exact results for the isotropic spin-$1/2$ Heisenberg chain with dissipative boundary driving”, TMF, 198:2 (2019), 341–362; Theoret. and Math. Phys., 198:2 (2019), 296–315
Linking options:
https://www.mathnet.ru/eng/tmf9556https://doi.org/10.4213/tmf9556 https://www.mathnet.ru/eng/tmf/v198/i2/p341
|
Statistics & downloads: |
Abstract page: | 306 | Full-text PDF : | 79 | References: | 24 | First page: | 5 |
|