Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in a Transverse Magnetic Field

We report on magnetization, sound velocity, and magnetocaloric-effect measurements of the Ising-like spin-1/2 antiferromagnetic chain system BaCo$_2$V$_2$O$_8$ as a function of temperature down to 1.3 K and applied transverse magnetic field up to 60 T. While across the N\'{e}el temperature of $T_N\sim5$ K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature the field-dependent measurements reveal a sharp softening of sound velocity $v(B)$ and a clear minimum of temperature $T(B)$ at $B^{c,3D}_\perp=21.4$ T, indicating the suppression of the antiferromagnetic order. At higher fields, the $T(B)$ curve shows a broad minimum at $B^c_\perp = 40$ T, accompanied by a broad minimum in the sound velocity and a saturation-like magnetization. These features signal a quantum phase transition which is further characterized by the divergent behavior of the Gr\"{u}neisen parameter $\Gamma_B \propto (B-B^{c}_\perp)^{-1}$. By contrast, around the critical field, the Gr\"{u}neisen parameter converges as temperature decreases, pointing to a quantum critical point of the one-dimensional transverse-field Ising model.