Stacked quantum Ising systems and quantum Ashkin-Teller model

We analyze the quantum states of an isolated composite system consisting of two stacked quantum Ising (SQI) subsystems, coupled by a local Hamiltonian term that preserves the Z₂ symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter w, with w=0 corresponding to decoupled quantum Ising systems. We focus on the quantum correlations of one of the two SQI subsystems, S, in the ground state of the global system, and study their dependence on both the state of the weakly-coupled complementary part E and the intercoupling strength. We concentrate on regimes in which S develops critical long-range correlations. The most interesting physical scenario arises when both SQI subsystems are critical. In particular, for identical SQI subsystems, the global system is equivalent to the quantum Ashkin-Teller model, characterized by an additional Z₂ interchange symmetry between the two subsystem operators. In this limit, one-dimensional SQI systems exhibit a peculiar critical line along which the length-scale critical exponent ν varies continuously with w, while two-dimensional systems develop quantum multicritical behaviors characterized by an effective enlargement of the symmetry of the critical modes, from the actual Z_2oplus Z₂ symmetry to a continuous O(2) symmetry.