In this paper, we have proved that there exists no translation invariant pure state of M=⊗k∈Z Md(k)(C) that is real, lattice symmetric with a certain twist and SU2(C) invariant for any even integer d ≥ 2. In particular, this result also shows that the Heisenberg iso-spin anti-ferromagnetic model with 12-odd integer spin degrees of freedom does not admit a unique ground state.

Journal of Mathematical PhysicsNov 1, 20183 citations

Preprint Series of Department of Mathematics, Hokkaido University

On the existence and uniqueness of ground states of the spin$B!>(Bboson Hamiltonian

A Aarai, Masao Hirokawa

Published Sep 1, 1995• 8 citations

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The existence and uniqueness of ground states of the spin-boson Hamiltonian

H_{\mathrm{S}\mathrm{B}}

are con- sidered.The main results in the case of massive bosons include:

(\mathrm{i})(\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e})

there exists a ground state without restriction for the strength of the coupling constant;

(\mathrm{i}\mathrm{i})(\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s})

under a mild (nonperturbative) condition for the parameters contained in

H_{\mathrm{S}\mathrm{B}},

H_{\mathrm{S}\mathrm{B}}

has only one ground state ; (iii) (degeneracy) under a certain condition for the parameters of

H_{\mathrm{S}\mathrm{B}}

which is weaker than that of (ii), the number of the ground states is at most two.In the case of massless bosons, the existence of a ground state of

H_{\mathrm{S}\mathrm{B}}

is shown as a limit of ground states of the massive case.The methods used are nonperturbative.A generalization of the model is proposed.