In order to study an interplay of disorder, correlation, and spin imbalance on antiferromagnetism, we systematically explore the ground state of one-dimensional spin-imbalanced Anderson-Hubbard model by using the density-matrix renormalization-group method. We find that disorders localize the antiferromagnetic spin-density wave induced by imbalanced fermions and the increase in the disorder magnitude shrinks the areas of the localized antiferromagnetized regions. Moreover, the antiferromagnetism finally disappears above a large disorder. The localization behaviors are observable in atomic Fermi gases loaded on optical lattices as broadening of the momentum distribution of the spin density by using the Stern-Gerlach type of time-of-flight imaging.In order to study an interplay of disorder, correlation, and spin imbalance on antiferromagnetism, we systematically explore the ground state of one-dimensional spin-imbalanced Anderson-Hubbard model by using the density-matrix renormalization-group method. We find that disorders localize the antiferromagnetic spin-density wave induced by imbalanced fermions and the increase in the disorder magnitude shrinks the areas of the localized antiferromagnetized regions. Moreover, the antiferromagnetism finally disappears above a large disorder. The localization behaviors are observable in atomic Fermi gases loaded on optical lattices as broadening of the momentum distribution of the spin density by using the Stern-Gerlach type of time-of-flight imaging.

arXiv:0810.3953Physical Review BMay 14, 20094 citations

Fluctuations of the two-dimensional quantum antiferromagnet in a disordered phase

V. I. Belinicher, João da Providência

May 11, 19990 citations

Ground state properties of the two-dimensional spin fermion model

Nobuo Furukawa, Masatoshi Imada

Physica C SuperconductivityDec 1, 19911 citation

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

M. Dudka, Andrei A. Fedorenko, Viktoria Blavatska +1 more

We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as $\ensuremath{\sim}{r}^{\ensuremath{-}a}$. Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $\ensuremath{\nu}=2/a+O({(2\ensuremath{-}a)}^{3})$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\ensuremath{\eta}}_{2}=1/2\ensuremath{-}(2\ensuremath{-}a)/4+O({(2\ensuremath{-}a)}^{2})$.We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as $\ensuremath{\sim}{r}^{\ensuremath{-}a}$. Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $\ensuremath{\nu}=2/a+O({(2\ensuremath{-}a)}^{3})$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\ensuremath{\eta}}_{2}=1/2\ensuremath{-}(2\ensuremath{-}a)/4+O({(2\ensuremath{-}a)}^{2})$.

arXiv:1602.07229Physical review. B./Physical review. BJun 22, 201625 citations

Disorder in a two-dimensional quantum spin liquid

D. Hüvonen, Martin Må̊nsson, S. N. Gvasaliya +8 more

Bulletin of the American Physical SocietyFeb 28, 20120 citations

Two-loop renormalization group calculation of response functions for a two-dimensional flat Fermi surface

Eberth de Almeida Correa, Hermann Freire, Álvaro Antônio Bandeira Ferraz

We present the formalism for a two-loop renormalization group (RG) calculation of some order-parameter susceptibilities associated with a two-dimensional (2D) flat Fermi-surface model. In this order of perturbation theory, one must take into account the self-energy effects directly in all RG flow equations. In one-loop order, our calculation reproduces the well-known results obtained previously by other RG schemes. That is, for repulsive interactions all susceptibilities diverge in the low-energy limit and the antiferromagnetic (AF) spin-density-wave correlations produce indeed the leading instability in the system. In contrast, in two-loop order, only the AF susceptibility diverges for this model. However, even this divergence takes place at a much slower rate than in the one-loop RG approach. The purpose of this paper is to show in a very simple setting how to assess the importance of two-loop quantum fluctuations in 2D interacting fermionic models. With some modifications, the present formalism can also be extended to discuss more realistic models such as the paradigmatic 2D Hubbard model.We present the formalism for a two-loop renormalization group (RG) calculation of some order-parameter susceptibilities associated with a two-dimensional (2D) flat Fermi-surface model. In this order of perturbation theory, one must take into account the self-energy effects directly in all RG flow equations. In one-loop order, our calculation reproduces the well-known results obtained previously by other RG schemes. That is, for repulsive interactions all susceptibilities diverge in the low-energy limit and the antiferromagnetic (AF) spin-density-wave correlations produce indeed the leading instability in the system. In contrast, in two-loop order, only the AF susceptibility diverges for this model. However, even this divergence takes place at a much slower rate than in the one-loop RG approach. The purpose of this paper is to show in a very simple setting how to assess the importance of two-loop quantum fluctuations in 2D interacting fermionic models. With some modifications, the present formalism can also be extended to discuss more realistic models such as the paradigmatic 2D Hubbard model.

Physical Review BNov 10, 20087 citations

0.995<a<2

and is characterized by the correlation length exponent $\ensuremath{\nu}=2/a+O({(2\ensuremath{-}a)}^{3})$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\ensuremath{\eta}}_{2}=1/2\ensuremath{-}(2\ensuremath{-}a)/4+O({(2\ensuremath{-}a)}^{2})$.