Phase transition of Kitaev spin liquid described by quantum geometric tensor
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912172649480192 |
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| author | Lu, Meng-Meng Wang, Zheng-Chuan |
| author_facet | Lu, Meng-Meng Wang, Zheng-Chuan |
| contents | Weinvestigate the topological phase transition of Kitaev spin liquid in an external magnetic field by calculating
the Berry curvature and the Fubini-Study metric. Employing Jordan-Wigner transformation and effective
perturbative theory to transform the Hamiltonian into fermionic quadratic form, the Berry curvature is calculated
by choosing the effective magnetic field as the parameter, and we find that the xy-component of the Berry
curvature has the same behavior around the critical lines with the phase diagram and the behavior of Berry
curvature around the critical line will not be influenced by local perturbation, i.e. it has the robustness against
the local perturbation. Especially, we relate the Berry curvature with the derivative of effective magnetic
susceptibility which can be regarded as the signature of topological phase transition besides, we related the
second nonlinear susceptibility with the non-Abelian Berry connection. Then we analytically calculate the
generalized Berry curvature in the mixed state called mean Uhlmann curvature which can be related with the
spectral function, the curves that mean Uhlmanncurvaturechangingtemperaturewithdifferentcouplingconstant
reveal that it will have an extrema when adjust $J_x$ from $A$ phase to $B$ phase. At last we analytically calculate the
quantum geometric tensor in the effective magnetic field space whose imaginary part is the Berry curvature and
real part is the Fubini-Study metric, and we find that the zz-component of Fubini-Study metric and the phase
diagram are highly correlated which will peak at the cross point of three phases, then the Fubini-Study metric
is extended to the finite temperature with arising an additional term called Fisher-Rao metric caused by mixed
state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase transition of Kitaev spin liquid described by quantum geometric tensor Lu, Meng-Meng Wang, Zheng-Chuan Strongly Correlated Electrons Weinvestigate the topological phase transition of Kitaev spin liquid in an external magnetic field by calculating the Berry curvature and the Fubini-Study metric. Employing Jordan-Wigner transformation and effective perturbative theory to transform the Hamiltonian into fermionic quadratic form, the Berry curvature is calculated by choosing the effective magnetic field as the parameter, and we find that the xy-component of the Berry curvature has the same behavior around the critical lines with the phase diagram and the behavior of Berry curvature around the critical line will not be influenced by local perturbation, i.e. it has the robustness against the local perturbation. Especially, we relate the Berry curvature with the derivative of effective magnetic susceptibility which can be regarded as the signature of topological phase transition besides, we related the second nonlinear susceptibility with the non-Abelian Berry connection. Then we analytically calculate the generalized Berry curvature in the mixed state called mean Uhlmann curvature which can be related with the spectral function, the curves that mean Uhlmanncurvaturechangingtemperaturewithdifferentcouplingconstant reveal that it will have an extrema when adjust $J_x$ from $A$ phase to $B$ phase. At last we analytically calculate the quantum geometric tensor in the effective magnetic field space whose imaginary part is the Berry curvature and real part is the Fubini-Study metric, and we find that the zz-component of Fubini-Study metric and the phase diagram are highly correlated which will peak at the cross point of three phases, then the Fubini-Study metric is extended to the finite temperature with arising an additional term called Fisher-Rao metric caused by mixed state. |
| title | Phase transition of Kitaev spin liquid described by quantum geometric tensor |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2412.20889 |