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Physics Letters A

Invariant Hermitian operator and geometric phase for the Heisenberg spin system in a time-dependent magnetic field

Fengli Yan, Linguang Yang, Bo‐Zang Li

Published Aug 1, 1999• 12 citations
Publisher
DOI
10.1016/s0375-9601(99)00423-5

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1 On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field

Ali Mostafazadeh

We consider a class of general spin Hamiltonians of the form $H_s(t)=H_0(t)+H'(t)$ where $H_0(t)$ and $H'(t)$ describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the spins, respectively. We show that if $H'(t)$ is rotationally invariant, then $H_s(t)$ admits the same dynamical invariant as $H_0(t)$. A direct application of this observation is a straightforward rederivation of the results of Yan et al [Phys. Lett. A, Vol: 251 (1999) 289 and Vol: 259 (1999) 207] on the Heisenberg spin system in a changing magnetic field.

•Jan 1, 2001•0 citations
We consider a class of general spin Hamiltonians of the form Hs(t)=H0(t)+H′(t)H_s(t)=H_0(t)+H'(t)Hs​(t)=H0​(t)+H′(t) where H0(t)H_0(t)H0​(t) and H′(t)H'(t)H′(t) describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the spins, respectively. We show that if H′(t)H'(t)H′(t) is rotationally invariant, then Hs(t)H_s(t)Hs​(t) admits the same dynamical invariant as H0(t)H_0(t)H0​(t). A direct application of this observation is a straightforward rederivation of the results of Yan et al [Phys. Lett. A, Vol: 251 (1999) 289 and Vol: 259 (1999) 207] on the Heisenberg spin system in a changing magnetic field.