Stacked quantum Ising systems and quantum Ashkin-Teller model

TL;DR

This paper investigates the quantum correlations and critical behaviors of stacked quantum Ising systems, revealing novel critical lines and multicritical points related to the quantum Ashkin-Teller model.

Contribution

It provides a detailed analysis of the quantum states and correlations in coupled quantum Ising systems, especially at criticality, connecting to the quantum Ashkin-Teller model.

Findings

Critical lines with continuously varying exponents in 1D systems.

Quantum multicritical behaviors with enlarged symmetry in 2D systems.

Dependence of quantum correlations on coupling strength and subsystem states.

Abstract

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 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 $Z_2$ 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 $\nu$ 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 $Z_2\oplus Z_2$ symmetry to a continuous O(2) symmetry.