The magnetic-field-induced transition in a spin S = 1/2 one-dimensional (1D) magnet with Ising anisotropy under a transverse field is a prototypical example of a quantum phase transition driven by quantum fluctuations near absolute zero. Because the Zeeman term associated with a transverse magnetic field applied perpendicular to the Ising axis does not commute with the Hamiltonian of the Ising interaction, the field introduces quantum fluctuations into the spin chain. Thus, the magnetic order in the spin chain is gradually disturbed by applying the transverse field and is completely suppressed at the specific critical field H_c. Upon increasing the field to H_c, the ground state wave function of the spin chain becomes highly entangled and transforms into a quantum critical state with the logarithmic divergence of the entanglement entropy with respect to the chain length at H_c. Finally, the spin chain enters a quantum disordered state with an exponential decay of the spin correlation function above H_c. This nontrivial quantum phase transition, driven by a continuously tunable parameter in a comparatively simple system, has been intensively examined theoretically.

 We examine the quantum phase transition through high-field electron spin resonance measurements of an idealized model substance for the S = 1/2 quasi-1D Ising antiferromagnet CsCoCl₃, specifically via observations of the magnetic excitation. This Zeeman ladder comprises several discrete energy levels arising from the energy continuum of spinon excitations inherent to the antiferromagnetic quantum spin chain. The Zeeman ladder energy levels, spanning a wide frequency range exceeding 2000 GHz under zero magnetic field, gradually converge toward each other upon increasing the transverse field. At H_c, the Zeeman ladder becomes softened and evolves into a magnon mode with a single dispersion curve. In the magnetically ordered state below H_c, the spin chain exhibits a finite energy gap between the ground and excited states, which stabilizes the order against disturbances arising from quantum fluctuations. Above H_c, the system transitions to a paramagnetic state characterized by an exponential decay of spin correlations, which also remains gapped. In contrast, at the critical point H_c, which separates these two qualitatively distinct gapped states, the spin chain becomes gapless and enters a quantum critical state characterized by an algebraic decay of the correlation function. To drive the spin chain into this gapless quantum critical state, the spinon excitation becomes softened and its energy continuum is suppressed at H_c. This behavior is supported by detailed density matrix renormalization group calculations.

(Written by Shojiro Kimura on behalf of all the authors)

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