We present a functional renormalization group calculation for the two-dimensional $(t,{t}^{\ensuremath{'}})$-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependencies we find higher pseudocritical scales and a smaller region of $d$ -wave superconductivity. A large contribution to the effective interaction is given by a forward-scattering process with finite frequency exchange. We test different frequency parametrizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.We present a functional renormalization group calculation for the two-dimensional $(t,{t}^{\ensuremath{'}})$-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependencies we find higher pseudocritical scales and a smaller region of $d$-wave superconductivity. A large contribution to the effective interaction is given by a forward-scattering process with finite frequency exchange. We test different frequency parametrizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.

arXiv:1111.6802Physical Review BFeb 21, 201262 citations

A gauge invariant dressed holon and spinon description of the normal state of underdoped cuprates

Shiping Feng, Jihong Qin, Tianxing Ma

A partial charge-spin separation fermion-spin theory is developed to study the normal-state properties of the underdoped cuprates. In this approach, the physical electron is decoupled as a gauge invariant dressed holon and spinon, with the dressed holon behaving like a spinful fermion, and represents the charge degree of freedom together with the phase part of the spin degree of freedom, while the dressed spinon is a hard-core boson, and representing the amplitude part of the spin degree of freedom. The electron local constraint for single occupancy is satisfied. Within this approach, the charge and spin dynamics of the underdoped cuprates are studied based on the t-t'-J model. It is shown that the charge dynamics is mainly governed by the scattering from the dressed holons due to the dressed spinon fluctuation, while the scattering from the dressed spinons due to the dressed holon fluctuation dominates the spin dynamics.A partial charge-spin separation fermion-spin theory is developed to study the normal-state properties of the underdoped cuprates. In this approach, the physical electron is decoupled as a gauge invariant dressed holon and spinon, with the dressed holon behaving like a spinful fermion, and represents the charge degree of freedom together with the phase part of the spin degree of freedom, while the dressed spinon is a hard-core boson, and representing the amplitude part of the spin degree of freedom. The electron local constraint for single occupancy is satisfied. Within this approach, the charge and spin dynamics of the underdoped cuprates are studied based on the t-t'-J model. It is shown that the charge dynamics is mainly governed by the scattering from the dressed holons due to the dressed spinon fluctuation, while the scattering from the dressed spinons due to the dressed holon fluctuation dominates the spin dynamics.

arXiv:cond-mat/0304042Journal of Physics Condensed MatterJan 9, 2004110 citations

Partial Bosonisation of Fermions

Stellan S. Ostlund, Mats Granath

Jul 11, 20050 citations

Umklapp scattering in the one-dimensional Hubbard model

Tong Liu, Kang Wang, Runze Chi +3 more

The one-dimensional Mott metal-insulator transition is a typical strong correlation effect triggered by the Umklapp scattering. However, in a physical system, the Umklapp scattering coexists with the normal scattering, including both forward and backward scattering, which conserves the total momentum of scattered electrons. Therefore, it is not easy to quantify the contribution of the Umklapp scattering in a Mott metal-insulator transition. To resolve this difficulty, we propose to explore these scattering processes separately. We study the contribution of each scattering process in the one-dimensional Hubbard model using the momentum-space density-matrix renormalization group (kDMRG) and bosonization methods. Our kDMRG calculation confirms that the Mott charge gap results from the Umklapp scattering, but the normal scattering processes strongly renormalize its value. Furthermore, we present a scaling analysis of the Mott charge gap in the bosonization theory and show that the interplay between the Umklapp and forward scattering dictates the charge dynamics in the half-filled Hubbard model.The one-dimensional Mott metal-insulator transition is a typical strong correlation effect triggered by the Umklapp scattering. However, in a physical system, the Umklapp scattering coexists with the normal scattering, including both forward and backward scattering, which conserves the total momentum of scattered electrons. Therefore, it is not easy to quantify the contribution of the Umklapp scattering in a Mott metal-insulator transition. To resolve this difficulty, we propose to explore these scattering processes separately. We study the contribution of each scattering process in the one-dimensional Hubbard model using the momentum-space density-matrix renormalization group (kDMRG) and bosonization methods. Our kDMRG calculation confirms that the Mott charge gap results from the Umklapp scattering, but the normal scattering processes strongly renormalize its value. Furthermore, we present a scaling analysis of the Mott charge gap in the bosonization theory and show that the interplay between the Umklapp and forward scattering dictates the charge dynamics in the half-filled Hubbard model.

arXiv:2212.10972Physical review. B./Physical review. BSep 21, 20231 citation

Bosonization of fermion interaction

Seiju Ami

Sep 13, 19960 citations

d

-wave superconductivity. A large contribution to the effective interaction is given by a forward-scattering process with finite frequency exchange. We test different frequency parametrizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.