Abstract
The presence of disorders in frustrated spin glass offers conflict in spin ordering. As a result, the hopping electron is unable to complete a closed path. We have pointed out that a different kind of Berry connection is developed in a frustrated spin system. The developed Berry phase in the frustrated spin system departs from the usual solid angle, but the two are identical under special conditions. Further, the chiral change of helicity of a quantized spinor is prominent only in the presence of frustration. We show how the Berry phase is able to reveal the disordered character of systems such as spin glasses.
Highlights
In the theory of spin glasses, the concept of frozen spin configuration and frustration have played an important role [1]
If we consider the triangular frustrated lattice the frustrated function will be φijk = Aij + Ajk + Aki = Aij. It seems that this sum over link gauge degree of freedom ij Aij gives rise in the continuum limit the connection over a closed path.This implies that a frustrated function is equivalent to the net change of curvature over the closed path measured through Berry phase
The phase aij is the vector potential generated by the spin,and corresponds to the Berry phase felt by the hopping electron
Summary
In the theory of spin glasses, the concept of frozen spin configuration and frustration have played an important role [1]. It seems that this sum over link gauge degree of freedom ij Aij gives rise in the continuum limit the connection over a closed path.This implies that a frustrated function is equivalent to the net change of curvature over the closed path measured through Berry phase. | ↓ (t) = (− cos θ |0 + sin θ e−iφ|1 )ei/2(φ+χ) giving rise in similar manner the Berry phase over the closed path γ↓ = −iπ(1 − cos θ)
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