Quantum Theory of Many-Body Systems

Alexandre M. Zagoskin

Benjamin Schlein

We review some recent applications of rigorous Bogoliubov theory. We show how Bogoliubov theory can be used to approximate quantum fluctuations, both in the analysis of the energy spectrum and in the study of the dynamics of many-body quantum systems.

Alexandre M. Zagoskin

Yongdan Yang, Zongkang Zhang, Xiaosi Xu +2 more

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the original theories. Here the central tasks are finding the optimal effective theories and proving their equivalence to the original theories. Recently quantum computing has shown the potential of solving quantum many-body systems by exploiting its inherent parallelism. It is thus an interesting topic to discuss the emergence of effective theories and design efficient tools for finding them based on the results from quantum computing. As the first step towards this direction, in this paper, we propose two approaches that apply quantum computing to find the optimal effective theory of a quantum many-body system given its full Hamiltonian. The first algorithm searches the space of effective Hamiltonians by quantum phase estimation and amplitude amplification. The second algorithm is based on a variational approach that is promising for near-future applications.

Luca Salasnich

Aditi Sen, Ujjwal Sen

The mean-field theory, in its different hues, forms a useful tool for investigating single-body properties, like magnetization and susceptibility, of many-body systems. We propose an "entanglement mean-field theory", which transforms a many-body system into a two-body one, while retaining footprints of the many-body parent, using which it is possible to examine its two-body properties, and predict temperature-driven as well as quantum fluctuation-driven critical phenomena, by considering two-body self-consistency equations in contrast to single-body ones in mean-field–like theories. Compared to mean-field theory, the proposed one, with little to no extra complicacy, makes better predictions for the critical points, as well as for the qualitative and quantitative behavior of single- and two-body physical quantities. In particular, the predictions of the proposed theory are in much better conformity with the Curie-Weiss law for magnetization. Also, the proposed theory predicts an order by disorder for a correlation function in the random-field transverse quantum Ising model.