Many-Body Theory in One Dimension

Manuel Valiente

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.

Hermann G. Kümmel, MANFRED L. RISTIG

Oleksandr Tsyplyatyev, Peter Kopietz, Yee Kin Tsui +7 more

We construct a many-body theory of magnetoelasticity in one dimension and show that the dynamical correlation functions of the quantum magnet, connecting the spins with phonons, involve all energy scales. Accounting for all magnetic states nonperturbatively via the exact diagonalization techniques of Bethe ansatz, we find that the renormalization of the phonon velocity is a nonmonotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons---via hybridization with the continuum of excitations at high energy. We conduct ultrasonic measurements on a high-quality single crystal of the frustrated spin-1/2 Heisenberg antiferromagnet ${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$ in its nearly one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.

J W Clark, MANUEL DE LLANO, Mauricio Fortes +1 more

Collective

R. F. Bishop, John B. Parkinson, Yang Xian

The coupled-cluster method of many-body theory is applied to anisotropic quantum antiferromagnets in one and two dimensions. It is found to give good results for ground-state and excited-state energies and the staggered magnetization. It also gives a qualitatively correct description of the entire one-dimensional Heisenberg-Ising phase and the phase change in one dimension as the anisotropy decreases.