Lecturer: Zsolt Gulacsi

Keywords: Exact ground states, non-integrable many-body systems, Hamiltonian cast in positive semidefinite form

Abstract: The method we developed is based on the transformation of the Hamiltonian (H) in positive semidefinite form H = P + c, where P is a positive semidefinite operator, while c is a scalar. After this step the ground state is deduced by constructing the most general wave vector |v>, which satisfies the P |v> =0 property. The uniqueness is proven, and by calculating proper ground state expectation values, the physical properties of the system are deduced. If the ground state is obtained in a total particle number dependent manner, exact results can be provided also for the low laying part of the excitation spectrum e.g. via the particle number dependent chemical potential which can be connected to the charge gap. The different steps of the technique will be presented in details, and the results will be illustrated by applications on various systems.

References:

[1] Z. Gulacsi, Phys. Rev. B66, 165109 (2002) 

[2] Z. Gulacsi, D. Vollhardt, Phys. Rev. Lett. 91, 186401 (2003); and Phys. Rev. B72. 075130 (2005)

[3] Z. Gulacsi, Phys. Rev. B69, 054204 (2004).

[4] Z. Gulacsi, A. Kampf, D. Vollhardt, Phys. Rev. Lett. 99, 026404 (2007); and Prog. Theor. Phys. Suppl. 176, 1, (2008)

[5] Z. Gulacsi, Phys. Rev. B77, 245113 (2008)

[6] Z. Gulacsi, A. Kampf, D. Vollhardt, Phys. Rev. Lett. 105, 266403 (2010)

[7] Z. Gulacsi, Int. Jour. Mod. Phys. B27, 1330009 (2013) 

[8] Z. Gulacsi, Int. Jour. Math. Mod. Meth. Appl. Sci. 9, 691 (2015)