Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

Abstract

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/\Gamma \to \infty$, $\Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\Gamma >0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\Gamma$ the transition is of mixed-order.

arXiv comment8 pages, 2 tables and 8 figures

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• Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields
• First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain
• Random Ising chain in transverse and longitudinal fields: Strong disorder RG study
• Pattern Description of Quantum Phase Transitions in the Transverse Antiferromagnetic Ising Model with a Longitudinal Field
• Random transverse and longitudinal field Ising chains
• Quantum Potts chain in alternating field