2017/05/31 by Álvaro Gómez-León
Physics and Astronomy · #Condensed matter physics #Decoupling (probability) #Equations of motion #Ising model #MAJORANA #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Spins #Statistical physics #Superconductivity #Theoretical and Computational Physics #Thermal fluctuations #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.064426
published as Phys. Rev. B 96, 064426 (2017) · 10 pages, 7 figures
openalex created_date 2017/05/19 · openalex publication_date 2017/08/21 · arxiv created 2017/10/12 · arxiv updated 2017/10/13 · openalex updated_date 2026/08/05
We study the quantum Ising model in D dimensions with the equation-of-motion technique and the Majorana representation for spins. The decoupling scheme used for the Green's functions is based on the hierarchy of correlations in position space. To lowest order, this method reproduces the well-known mean field phase diagram and critical exponents. When correlations between spins are included, we show how the appearance of thermal fluctuations and magnons strongly affects the physical properties. In one dimension and for B=0 we demonstrate that, to first order in correlations, thermal fluctuations completely destroy the ordered phase. For nonvanishing transverse field we show that the model exhibits different behavior than its classical counterpart, especially near the quantum critical point. We discuss the connection with the Dyson's equation formalism and the explicit form of the self-energies.