Correlation Inequalities for Quantum Spin Systems with Quenched Centered Disorder

TL;DR

This paper extends classical correlation inequalities to quantum spin systems with centered disorder, demonstrating their implications for thermodynamic limits and boundary conditions.

Contribution

It introduces correlation inequalities for quantum spin systems with quenched centered disorder, previously known only in classical models.

Findings

Monotone convergence of pressure and ground state energy to the thermodynamic limit.

Bounds on surface pressures for various boundary conditions.

Validation of correlation inequalities in the quantum setting.

Abstract

It is shown that random quantum spin systems with centered disorder satisfy correlation inequalities previously proved (arXiv:cond-mat/0612371) in the classical case. Consequences include monotone approach of pressure and ground state energy to the thermodynamic limit. Signs and bounds on the surface pressures for different boundary conditions are also derived for finite range potentials.