Field-Induced Ising Criticality and Incommensurability in Anisotropic Spin-1 Chains

Quantum phase transitions induced by an external magnetic field in the Haldane-gapped spin-1 chains are studied in a fermionic field-theoretic description of the model. In the case with broken axial symmetry, two transitions occurs consecutively as increasing the field: $h_c=(m_1{m}_2{)}^{1\mathrm{/}2}$ (with $m_1$ and $m_2$ the transverse masses) is the critical Ising point and ${\tilde{h}}_c^{\ast }(>h_c)$ is the commensurate-incommensurate transition point. Although the latter is thermodynamically indiscernible, its property is revealed in the spin correlation functions (both uniform and staggered) which are calculated upon expressing the correlations of coupled Ising pair fields in terms of block-Toeplitz determinants.