Exact results for some non-integrable models of interacting spins and bosons

Fabian H. L. Eßler, Gora V. Shlyapnikov, Alexei M. Tsvelik

We consider a model of one-dimensional spin-1 bosons with repulsive density–density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin–charge separated theory of a Tomonaga–Luttinger Hamiltonian and the O(3) non-linear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density–density to spin–spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.

N. M. Bogoliubov, R. Bullough

Hans-Peter Eckle

N. M. Bogoliubov, Andrei V. Rybin, JUSSI TIMONEN

A composite quantum model on a lattice which describes the system of q-bosons interacting with U q (su(2)) spin impurities is introduced and solved exactly under periodic boundary conditions. In one limit the model is shown to become a new exactly soluble quantum system on a lattice which can be interpreted as a q-deformed version of the quantum Dicke model. In the limit of infinitesimal spacing the model is further reduced to a multilevel version of the previously introduced continuum-limit Dicke model. For spin 1/2 the previous results for this particular case are confirmed.

Luigi Amico A, Holger Frahm, Andreas Osterloh +1 more

Aidan Strathearn, B W Lovett, P Kirton

Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.