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The ground state phase diagrams and thermodynamic properties of a spin-1bond-alternating Heisenberg antiferromagnetic chain with a single-ionanisotropy in longitudinal and transverse magnetic fields are investigatedjointly by means of the infinite time evolving block decimation, the linearizedtensor renormalization group and the density matrix renormalization groupmethods. It is found that in the magnetic field-bond alternating ratio planesix phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2magnetization plateau and spin polarized phases are identified in alongitudinal field, while in a transverse field there are fives phasesincluding singlet dimer, Haldane, Z$_2$ symmetry breaking, quasi-1/2magnetization plateau and quasi spin polarized phases. A reentrant behavior ofthe staggered magnetization in a transverse field is observed. The quantumcritical behaviors in longitudinal and transverse magnetic fields are disclosedto fall into different universality classes with corresponding conformal fieldcentral charge $c=1$ and 1/2, respectively. The experimental data of thecompound NTENP under both longitudinal and transverse magnetic fields arenicely fitted, and the Luttinger liquid behavior of low temperature specificheat experimentally observed is also confirmed.

Phase Diagrams, Distinct Conformal Anomalies and Thermodynamics of Spin-1 Bond-Alternating Heisenberg Antiferromagnetic Chain in Magnetic Fields