arXiv:1110.4952 · The European Physical Journal B

Geometric phase in the Kitaev honeycomb model and scaling behaviour at critical points

J. Lian, J. -Q. Liang, G. Chen

Published Jun 1, 2012• 5 citations

arXiv HTML PDF

DOI: 10.1140/epjb/e2012-20901-1

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arXiv:1110.4952 · The European Physical Journal B

Geometric phase in the Kitaev honeycomb model and scaling behaviour at critical points

J. Lian, J. -Q. Liang, G. Chen

Published Jun 1, 2012• 5 citations

arXiv HTML PDF

DOI: 10.1140/epjb/e2012-20901-1

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Dynamical merging of Dirac points in the periodically driven Kitaev honeycomb model

Utso Bhattacharya, Sayak Dasgupta, Amit Dutta

arXiv:1508.04598The European Physical Journal BOct 1, 20169 citations

Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model

Guoyi Zhu, Markus Heyl

Bulletin of the American Physical SocietyMar 18, 20210 citations

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Sei-ichiro Suga, Takafumi J. Suzuki, Takuto Yamada

Bulletin of the American Physical SocietyMar 5, 20200 citations

Quantum fidelity in Tomonaga-Luttinger liquid and Kitaev model in the thermodynamic limit

Victor Mukherjee, Amit Dutta, Diptiman Sen

We study the scaling behavior of the fidelity (F ) in the thermodynamic limit using the examples of a Tomonaga-Luttinger liquid in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow powerlaw scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The behavior of F inside the gapless phase of the Kitaev model is found to depend strongly on its distance from the anisotropic quantum critical point. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for angle of rotation η and η+ dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.We study the scaling behavior of the fidelity (F ) in the thermodynamic limit using the examples of a Tomonaga-Luttinger liquid in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow powerlaw scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The behavior of F inside the gapless phase of the Kitaev model is found to depend strongly on its distance from the anisotropic quantum critical point. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for angle of rotation η and η+ dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

APSAug 12, 20110 citations

Topological quantum phase transitions in the 2-D Kitaev honeycomb model

Qi Chen, Guo-Qing Zhang, Jun-Qing Cheng +1 more

Quantum Information ProcessingNov 19, 201813 citations

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

Victor Mukherjee, Amit Dutta, Diptiman Sen

We study the scaling behavior of the fidelity ( $F$ ) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of $F$ for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of $F$ inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the $z$ axis and calculate $F$ through the overlap between the ground states for the angle of rotation $\ensuremath{\eta}$ and $\ensuremath{\eta}+d\ensuremath{\eta}$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.We study the scaling behavior of the fidelity ($F$) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of $F$ for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of $F$ inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the $z$ axis and calculate $F$ through the overlap between the ground states for the angle of rotation $\ensuremath{\eta}$ and $\ensuremath{\eta}+d\ensuremath{\eta}$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

arXiv:1108.2597Physical Review BJan 3, 201225 citations

We study the scaling behavior of the fidelity (

F

) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of

F

for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of

F

inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the

z

axis and calculate

F

through the overlap between the ground states for the angle of rotation $\ensuremath{\eta}$ and $\ensuremath{\eta}+d\ensuremath{\eta}$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.