a Study of Two-Dimensional Quantum Many-Body Systems.

Joaquín E. Drut, J. R. McKenney, W. S. Daza +2 more

We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.

Vedene H. Smith

Irving E. Segal, D. J. Thouless

Peter Degenfeld-Schonburg, Michael J. Hartmann

The description of quantum many-body systems is an exceedingly cumbersome challenge since the dimensions of their Hilbert spaces scale exponentially with the number of constituents. Whereas mean-field approaches are expected to provide accurate descriptions for high dimensional lattices, numerical approaches based on the density matrix renormalization group have very successfully been applied to one-dimensional chains. Yet for two-dimensional lattices there is still a pressing need for efficient descriptions as these are expected to host some very intriguing but still illusive phenomena in quantum many-body physics. Here we derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based approach is thus highly efficient and not restricted to unitary dynamics. We show its excellent accuracy for moderate size one-dimensional and small two-dimensional systems where very accurate or exact numerical solutions are available.

Pranjal Bordia, Henrik Lüschen, Sebastian Scherg +4 more

While many-body localization is well understood in one-dimensional systems, its behavior in two or more dimensions is largely unknown. New experiments hint at a many-body localized phase in a two-dimensional system and provide insight into how a system transitions between this phase and a normal thermal phase.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng