Quantum criticality and confinement effects in an Ising chain in transverse field

M. Hälg, D. Hüvonen, T. Guidi +4 more

J. M. Luck

Ying Wang

We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an ex-perimentally accessible physical implementation,a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line reso-nator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two mag-netic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally in-dependent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus,the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.

Ladislav Šamaj, Zoltán Bajnok

Xiao Wang, Jianda Wu

Near $(1+1)$-dimensional [$(1+1)$D] Ising criticality, a magnetic perturbation induces confinement and produces a cascade of bound-state excitations known as mesons. Here we show these mesons share a universal mass scaling after independently rescaling the model-dependent microscopic couplings. The number of stable mesons is controlled by the lightest two-meson threshold, while the lightest-meson mass follows a continuous trajectory characterized by a single scaling parameter. Using Hamiltonian truncation method, we obtain the trajectory numerically in both Ising field theory and the near-critical mixed-field Ising chain (MFIC). Under the rescaling, the trajectory and stable-meson-count crossover windows of MFIC both collapse onto the field-theory results. To further demonstrate the above universal organization of the meson spectra, we consider a class of four-periodic spin-$1/2$ Heisenberg-Ising chains under transverse fields, whose parameter space contains a family of quantum Ising critical points. The Hamiltonian family includes effective spin models for the quasi-one-dimensional antiferromagnets Ba(Sr)Co$_2$V$_2$O$_8$. Using tensor-network calculations, we obtain the corresponding lightest-meson mass trajectory for BaCo$_2$V$_2$O$_8$ and find that it also collapse onto the same universal curve given by field-theory result. Our results suggest that the universal scaling structure of quantum Ising criticality extends into the nearby confining regime, governing the organization of the meson spectrum. They thereby provide a practical criterion for interpreting excitations of quasi-1D Ising-like magnets in mixed fields beyond $E_8$ integrability.

Lei 磊 Xu 徐, Li‐Ping Yang

Abstract We study the role of Franck-Condon (F-C) principle in the dynamics of a central spin system, which is coupled to an Ising chain in transverse field. The transition process of energy levels caused by the excited central spin is studied to manifest the quantum critical effect through the Franck-Condon principle. The super-sensitivity of this quantum critical system is demonstrated clearly from the properties of Franck-Condon factors. We analytically show how spin numbers, coupling strength and order parameter of the Ising chain sensitively effect on the energy level populations in dynamical evolution near the critical point. This super-sensitivity and criticality are explicitly displayed in absorption spectrum .