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 Z 2 symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter w , with w = 0 corresponding to decoupled quantum Ising subsystems. 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 Z 2 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 discrete Z 2 ⊕ Z 2 symmetry to an effective continuous O(2) symmetry.