Quantum Many-Body Invited Talk

Federico Becca (ISAS-SISSA, Trieste)

Variational wave functions for strongly-correlated models

Variational wave functions represent a very powerful tool to study many-body systems, the Bardeen-Cooper-Schrieffer and Laughlin states being two important examples. In this talk, I will show that extremely accurate wave functions can be constructed to describe the low-energy physics of magnetic systems in presence of frustrating interactions. This is a particularly interesting situation, since new exotic phases of matter may appear, such as spin liquids featuring topological order and elementary excitations with fractional quantum numbers. I will show that resonating-valence bond (RVB) states, constructed by using slave-particles approaches, strongly suggest that spin-liquid phases may be stabilized in the highly-frustrated regime of spin-1/2 Heisenberg models on Kagome and square lattices.

Furthermore, I will show how it is possible to study time-dependent problems (e.g., the real-time evolution of a generic initial state, the so-called quantum quenches) by using variational wave functions. The case of the Bose-Hubbard model is considered in one and two spatial dimensions, with particular emphasis on light-cone effects in the spreading of correlations. The accuracy of the variational method is benchmarked with state-of-the-art time-dependent density-matrix renormalization group calculations.

References :
– Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Physical Review B 87, 060405 (2013).
– W.-J. Hu, F. Becca, A. Parola, and S. Sorella, Physical Review B 88, 060402 (2013).
– Y. Iqbal, D. Poilblanc, and F. Becca, Physical Review B 89, 020407 (2014).
– G. Carleo, F. Becca, M. Schiro, and M. Fabrizio, Scientific Reports 2, 243 (2012).
– G. Carleo, F. Becca, L. Sanchez-Palencia, S. Sorella, and M. Fabrizio, Physical Review A 89, 031602 (2014).