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The Marshall condition in the ground state of frustrated quantum spin systems

Hidetsugu Kitatani, 北谷 英嗣

Published Jan 1, 1995• 0 citations
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Numerical and approximate analytical results for the frustrated spin- 1/2 quantum spin chain

Bursill, R., Gehring, G. A., DAMIAN J. J. FARNELL +3 more

We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

•Jan 1, 1995•110 citations
We consider the frustrated antiferromagnetic S = 1 Heisenberg quantum spin chain with regard to the Marshall-Peierls sign rule.Using exact diagonalization data we investigate the breakdown of the Marshall-Peierls sign rule in dependence on frustration and compare our findings with data for s = 1/2.We calculate a critical value of frustration J21" , where the Marshall-Peierls sign rule is violated.The extrapolation of this value to the infinite chain limit holds J?' s: 0.016, lower than in the case of s = 1/2 (J2crit 0.027).This points to a stronger influence of frustration in the case of s = 1.Nevertheless, the calculation of the weight of the Ising-states violating the Marshall-Peierls sign rule shows that the latter holds approximately even for a quite large frustration and may be used for numerical techniques.
We study the T=0 frustrated phase of the 1D quantum spin- 1/2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground-state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalization group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.