The phase diagram of quantum systems: Heisenberg antiferromagnets

Abstract

A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy and the correlation functions describing the effects of fluctuations on the thermodynamics of the system. These equations reproduce the full renormalization group structure in the neighborhood of a critical point keeping, at the same time, full information on the non universal properties of the model. As a concrete application we investigate the phase diagram of a Heisenberg antiferromagnet in a staggered external magnetic field. At long wavelengths the known relationship to the Quantum Non Linear Sigma Model naturally emerges from our approach. By representing the two point function in an approximate analytical form, we obtain a closed partial differential equation which is then solved numerically. The results in three dimensions are in good agreement with available Quantum Monte Carlo simulations and series expansions. More refined approximations to the general framework presented here and few applications to other models are briefly discussed.

17 pages, 7 figures

References in corpus (4)

• Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
• The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures
• Spin Correlations in the Two-Dimensional Spin-5/2 Heisenberg Antiferromagnet Rb2MnF4
• A microscopic approach to phase transitions in quantum systems

Cited by in corpus (8)

• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Thermodynamics of layered Heisenberg magnets with arbitrary spin
• Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
• Spin-distribution functionals and correlation energy of the Heisenberg model
• Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach
• Self-consistent Ornstein-Zernike approximation for three-dimensional spins
• Non linear sigma models and quantum spin systems
• The uniform quantized electron gas revisited