The application of the Schur-Weyl duality in the one-dimensional Hubbard model

We present the application of the Schur-Weyl duality in the one-dimensional Hubbard model in the case of half-filled system of any numer of atoms. We replace the actions of the dual symmetric and unitary groups in the whole Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the one-dimensional Hubbard model.Comment: 16 pages, 2 table

Fluctuations of imbalanced fermionic superfluids in two dimensions induce continuous quantum phase transitions and non-Fermi liquid behavior

We study the nature of superfluid pairing in imbalanced Fermi mixtures in two spatial dimensions. We present evidence that the combined effect of Fermi surface mismatch and order parameter fluctuations of the superfluid condensate can lead to continuous quantum phase transitions from a normal Fermi mixture to an intermediate Sarma-Liu-Wilczek superfluid with two gapless Fermi surfaces -- even when mean-field theory (incorrectly) predicts a first order transition to a phase-separated "Bardeen-Cooper-Schrieffer plus excess fermions" ground state. We propose a mechanism for non-Fermi liquid behavior from repeated scattering processes between the two Fermi surfaces and fluctuating Cooper pairs. Prospects for experimental observation with ultracold atoms are discussed.Comment: as accepted to Phys. Rev. X; 10 pages, 10 figures, 75 reference

Impact of Complementarity and Heterogeneity on Health Related Utility of Life

This study aims at identifying determinants of health related quality of life in Poland, and in particular at verifying whether health domains are complements or substitutes and what the impact of heterogeneity of population on the health state valuation is. The paper uses data in panel structure coming from a survey conducted in Poland and consisting of 6700 valuations (after data cleaning) of EQ-5D health states with time trade-off method. Several econometric models are built in order to detect the impact of complementarity and heterogeneity. Random effects models as well as random parameters models estimated using Bayesian approach are used. The results show that health domains are complementary goods. Especially the lack of pain/discomfort is a complement to other health domains. Demographic factors influence how health state change impacts utility. These factors encompass sex, education, respondent's health state and even belief in life after death.health related quality of life, QALY, EQ-5D, complementarity, heterogeneity