We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling.We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling.

arXiv:1307.3475Physical Review LettersMay 14, 2014140 citations

Renormalization group approach to the one-dimensional hubbard model

Hiroshi Takano, Masuo Suzuki

Physica A Statistical Mechanics and its ApplicationsDec 1, 19814 citations

The Numerical Renormalization Group applied to the Bose Hubbard Model

Sven Binder

Jan 1, 20070 citations

Strongly disordered Hubbard model in one dimension: Spin and orbital infinite randomness and Griffiths phases

R. Mélin, Ferenc Iglói

We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements ${t}_{min}<t<{t}_{max}$ , and with random onsite Coulomb repulsion terms $0\ensuremath{\leqslant}{U}_{min}<U<{U}_{max}$. There are two critical phases, corresponding to an infinite randomness spin random singlet for strong interactions $({U}_{min}>{t}_{max})$ and to an orbital infinite randomness fixed point for vanishing interactions $({U}_{max}∕{t}_{max}\ensuremath{\rightarrow}0)$. To each critical infinite randomness fixed point is connected a Griffiths phase, the correlation length, and dynamical exponent of which have well defined asymptotic dependences on the corresponding quantum control parameter. The theoretical predictions for the scaling in the vicinity of the critical points compare well to numerical RG simulations.We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements ${t}_{min}<t<{t}_{max}$, and with random onsite Coulomb repulsion terms $0\ensuremath{\leqslant}{U}_{min}<U<{U}_{max}$. There are two critical phases, corresponding to an infinite randomness spin random singlet for strong interactions $({U}_{min}>{t}_{max})$ and to an orbital infinite randomness fixed point for vanishing interactions $({U}_{max}∕{t}_{max}\ensuremath{\rightarrow}0)$. To each critical infinite randomness fixed point is connected a Griffiths phase, the correlation length, and dynamical exponent of which have well defined asymptotic dependences on the corresponding quantum control parameter. The theoretical predictions for the scaling in the vicinity of the critical points compare well to numerical RG simulations.

arXiv:cond-mat/0607269Physical Review BOct 4, 20066 citations

Functional renormalization group for fermion lattice models in three dimensions: Application to the Hubbard model on the cubic lattice

Jannis Ehrlich, Carsten Honerkamp A

The channel-decomposed functional renormalization group (FRG) approach, most recently presented in the variant of truncated-unity FRG (TUFRG), has so far been used for various two-dimensional model systems. Yet for many interesting material systems the third spatial dimension is of clear relevance. Therefore, FRG schemes working in three spatial dimensions (3D) are definitely on the wish list. Here we demonstrate that a 3D TUFRG scheme can be set up in a straightforward extension of previous two-dimensional codes and gives physically sensible results with affordable numerical effort, regarding both the qualitative and quantitative descriptions. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a $(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi})$-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a $d$ -wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.The channel-decomposed functional renormalization group (FRG) approach, most recently presented in the variant of truncated-unity FRG (TUFRG), has so far been used for various two-dimensional model systems. Yet for many interesting material systems the third spatial dimension is of clear relevance. Therefore, FRG schemes working in three spatial dimensions (3D) are definitely on the wish list. Here we demonstrate that a 3D TUFRG scheme can be set up in a straightforward extension of previous two-dimensional codes and gives physically sensible results with affordable numerical effort, regarding both the qualitative and quantitative descriptions. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a $(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi})$-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a $d$-wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.

arXiv:2004.14711Physical review. B./Physical review. BNov 5, 202019 citations

Real Space Numerical Renormalization Groups for Hubbard Models

Steven R. White

Springer proceedings in physicsJan 1, 19920 citations

We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements

{t}_{min}<t<{t}_{max}

, and with random onsite Coulomb repulsion terms $0\ensuremath{\leqslant}{U}_{min}<U<{U}_{max}$. There are two critical phases, corresponding to an infinite randomness spin random singlet for strong interactions

({U}_{min}>{t}_{max})

and to an orbital infinite randomness fixed point for vanishing interactions $({U}_{max}∕{t}_{max}\ensuremath{\rightarrow}0)$. To each critical infinite randomness fixed point is connected a Griffiths phase, the correlation length, and dynamical exponent of which have well defined asymptotic dependences on the corresponding quantum control parameter. The theoretical predictions for the scaling in the vicinity of the critical points compare well to numerical RG simulations.

d

-wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.