Series expansions for excited states of strongly correlated systems

Martin P. Gelfand

Valeri N. Kotov, Oleg P. Sushkov, Zheng Weihong +1 more

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ elementary excitations are described as a dilute Bose gas with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg antiferromagnet at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ with general couplings. Our analytic results for the triplet gap, the excitation spectrum, and the location of the quantum critical point are in excellent agreement with numerical results obtained by dimer series expansions.

Weihong Zheng, J. Oitmaa

We present results for the Kondo lattice model of strongly correlated electrons, in one, two, and three dimensions, obtained from high-order linked-cluster series expansions. Results are given for various ground-state properties at half filling, and for spin and charge excitations. Estimates for the location of the quantum critical point in the square and simple cubic lattices are made.

João da Providência, Carl M. Shakin

H. Monien

Guillaume Lang, F. W. J. Hekking, Anna Minguzzi

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan’s contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.