Nonlinear correlations of the susceptibility and multiparticle correlation functions

S. G. Tikhodeev

Puneet Sharma

Laurent P. Lévy, Andrew T. Ogielski

It is shown that the measurable nonlinear susceptibilities of third and higher orders probe only a fraction of equilibrium fluctuations, and in general can give only lower bounds on the equilibrium correlation functions. This contrasts with the linear and quadratic response, which completely determines the corresponding correlations by general fluctuation–dissipation theorems. The exactly solvable one-dimensional kinetic Ising model illustrates which fluctuations give rise to dissipation; only two-magnon processes of short wavelength and opposite momenta contribute to the third-order nonlinear susceptibilities, while two- and three-magnon processes contribute to the corresponding equilibrium correlation functions.

Andreas Rückriegel, Dmytro Tarasevych, Jan Krieg +1 more

We show that the high-temperature expansion of the free energy and arbitrary imaginary-time-ordered connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly written in closed form including all combinatorial factors. We use our method to estimate critical temperatures of Heisenberg magnets from low-order truncations of the inverse spin susceptibility in the static limit. We also calculate the connected correlation function involving three different spin components (chiral nonlinear susceptibility) of quantum Heisenberg magnets up to second order in the exchange couplings.

J. W. Halleý

M. Puoskari

We study a variational multiparticle correlation theory for the ground state of inhomogeneous Bose fluids at zerotemperature. The ground state wave function of a many-boson system is written as a generalized Jastrow–Feenberg function including multiparticle correlation functions. Euler–Lagrange equations for the one, two, three and four particle correlation functions are derived using a systematic functional theoretical approach within the framework of the generalized hypernetted chain theory (HNC2 equations). The Euler–Lagrange equations for the optimal one and two particle correlation functions are analyzed including the infinite series of the elementary diagrams summed by integral equations. For the determination of the optimal triplet correlation factor we propose a novel iterative procedure in which the HNC2 equation is used to calculate the triplet distribution function.