2000/04/14 by Pietro Gianinetti, Alberto Parola
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.63.104414
17 pages, 7 figures
arxiv created 2000/04/14 · openalex publication_date 2001/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An 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 nonuniversal 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 nonlinear \ensuremathσ 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.