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## Main Question or Discussion Point

Hi,

I am working on the Laughlin model of Quantum Hall Effect, which relates to the concept ' adiabatic curvature'. The paper didn't include much details, and I knew little about berry phase. Could some one please give me some idea that how is the local adiabatic curvature deduced? ( the expression of K below)

Here is the problem: consider a quantum Hamiltonian H(psi, theta). Suppose the Hamiltonian has a non-degenerate ground state at energy zero. Ground state is e^ia|phi(psi,theta)>, a is the initial phase that is free to choose. The local adiabatic curvature K of the bundle of ground states in the parameter space is defined as the limit of the Berry phase mismatch divided by the loop area, turns out to be

K = 2 Im < d(psi) phi| d(theta) phi> (here d indicates partial differential operator)

Thanks a lot.:)

I am working on the Laughlin model of Quantum Hall Effect, which relates to the concept ' adiabatic curvature'. The paper didn't include much details, and I knew little about berry phase. Could some one please give me some idea that how is the local adiabatic curvature deduced? ( the expression of K below)

Here is the problem: consider a quantum Hamiltonian H(psi, theta). Suppose the Hamiltonian has a non-degenerate ground state at energy zero. Ground state is e^ia|phi(psi,theta)>, a is the initial phase that is free to choose. The local adiabatic curvature K of the bundle of ground states in the parameter space is defined as the limit of the Berry phase mismatch divided by the loop area, turns out to be

K = 2 Im < d(psi) phi| d(theta) phi> (here d indicates partial differential operator)

Thanks a lot.:)