Kitaev Nanoribbon Model with Boundary Dephasing
ORAL
Abstract
In recent years, there has been a growing interest in the study of open quantum systems. Within the Markovian approximation, such systems are described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation [1, 2]. On the other hand, the Kitaev hon- eycomb model [3], which is known as an exactly solv- able example of a quantum spin liquid, has attracted considerable attention both theoretically and exper- imentally. However, its behavior in the presence of dissipation has not been clarified.
In this study, we assume that the time evolution is described by the GKSL equation and aim to clarify the effect of boundary dephasing on the Kitaev honeycomb model. As a first step, we consider boundary dephasing for the Kitaev nanoribbon model, which is a one-dimensional arrangement of hexagons in the Kitaev honeycomb model. By considering the effective non-Hermitian model by the Choi-Jamiolkwoski map [4], in which the density matrix in the GKSL equation is regarded as a vector, the Kitaev model with boundary dephasing can be solved using Kitaev’s Majorana fermion method.
Since the Majorana fermion method doubles the dimension of Hilbert space, it is necessary to consider restriction to the physical subspace. For open boundary conditions, we can eliminate the unphysical states by an appropriate gauge fixing. In the periodic case, it is necessary to compute the projection because unphysical states cannot be excluded by the gauge fixing. We have developed a method to compute the projection to the physical space systematically by extending the existing method [5] to the non-hermitian case.
The results for the Nanoribbon model show both numerically and analytically that for Jx = Jy case, the Liouvillian gap, which characterizes the relaxation time, decays with the square of the system size and becomes Liouvillian gapless in the thermodynamic limit. We also hope to report the results for the two-dimensional Kitaev honeycomb model with boundary dephasing.
[1] G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
[2] V. Gorini, A. Kossakowski and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
[3] A. Kitaev, Ann. Phys. 321, 2 (2006).
[4] F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Phys. Rev. A 98, 042118 (2018).
[5] F. L. Pedrocchi, S. Chesi, and D. Loss, Phys. Rev. B 84, 165414 (2011).
In this study, we assume that the time evolution is described by the GKSL equation and aim to clarify the effect of boundary dephasing on the Kitaev honeycomb model. As a first step, we consider boundary dephasing for the Kitaev nanoribbon model, which is a one-dimensional arrangement of hexagons in the Kitaev honeycomb model. By considering the effective non-Hermitian model by the Choi-Jamiolkwoski map [4], in which the density matrix in the GKSL equation is regarded as a vector, the Kitaev model with boundary dephasing can be solved using Kitaev’s Majorana fermion method.
Since the Majorana fermion method doubles the dimension of Hilbert space, it is necessary to consider restriction to the physical subspace. For open boundary conditions, we can eliminate the unphysical states by an appropriate gauge fixing. In the periodic case, it is necessary to compute the projection because unphysical states cannot be excluded by the gauge fixing. We have developed a method to compute the projection to the physical space systematically by extending the existing method [5] to the non-hermitian case.
The results for the Nanoribbon model show both numerically and analytically that for Jx = Jy case, the Liouvillian gap, which characterizes the relaxation time, decays with the square of the system size and becomes Liouvillian gapless in the thermodynamic limit. We also hope to report the results for the two-dimensional Kitaev honeycomb model with boundary dephasing.
[1] G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
[2] V. Gorini, A. Kossakowski and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
[3] A. Kitaev, Ann. Phys. 321, 2 (2006).
[4] F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Phys. Rev. A 98, 042118 (2018).
[5] F. L. Pedrocchi, S. Chesi, and D. Loss, Phys. Rev. B 84, 165414 (2011).
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Presenters
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Shunta Kitahama
The University of Tokyo
Authors
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Shunta Kitahama
The University of Tokyo
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Hosho Katsura
The University of Tokyo
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Naoyuki Shibata
The University of Tokyo