Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

High-resolution functional renormalization group calculations for interacting fermions on the square lattice

Julian Lichtenstein, David S 'anchez de la Pe na, Daniel Rohe, Edoardo Di Napoli, Carsten Honerkamp A

Published Mar 15, 2017• 0 citations
OpenAlex

Related papers

High-performance functional Renormalization Group calculations for interacting fermions

Julian Lichtenstein, David Sánchez de la Peña, D. Rohe +3 more

arXiv:1604.06296•Computer Physics Communications•Dec 26, 2016•96 citations

Functional Renormalization Group for Interacting Many-Fermion Systems on Two-Dimensional Lattices

Carsten Honerkamp A

Springer series in solid-state sciences•Aug 9, 2011•1 citation

Weakly correlated electrons on a square lattice: a renormalization group theory

Dražen Zanchi, Heinz J. Schulz

We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this method to the Hubbard model on a square lattice using both zero- and finite- temperature methods. Truncating the effective action at the sixth term in fermionic variables we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability Tc^{RG} as function of doping. We calculate furthermore the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type d while the AF fluctuations are of the type s Following the strength of both SC and AF fluctuation along the instability line we obtain the phase diagram. The temperature Tc^{RG} can be identified with the crossover temperature T{co} found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime Tc^{RG} corresponds to the superconducting critical temperature.

arXiv:cond-mat/9812303•Dec 17, 1998•0 citations

Weakly correlated electrons on a square lattice: Renormalization-group theory

Dražen Zanchi, Heinz J. Schulz

We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in the form of the Polchinski equation. The advantage of this renormalization scheme is that the flow itself has a physical interpretation, i.e., the cutoff has the meaning of the temperature. We apply this method to the Hubbard model on a square lattice using both zero- and finite-temperature methods. Truncating the effective action at the sixth term in fermionic variables and neglecting self-energy renormalization, we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability ${T}_{c}^{\mathrm{RG}}$ as a function of doping. Furthermore we calculate the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type ${d}_{{x}^{2}\ensuremath{-}{y}^{2}},$ while the AF fluctuations are of the type s. Following the strength of both SC and AF fluctuations along the instability line, we obtain the phase diagram. The temperature ${T}_{c}^{\mathrm{RG}}$ can be identified with the crossover temperature ${T}_{\mathrm{co}}$ found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime ${T}_{c}^{\mathrm{RG}}$ corresponds to the superconducting critical temperature.

Physical review. B, Condensed matter•May 15, 2000•222 citations

Block Renormalization Group Approach for Correlation Functions of Interacting Fermions

Emmanuel Pereira, Aldo Procacci

Letters in Mathematical Physics•Nov 1, 1997•0 citations

Untersuchungen von konkurrierenden Ordnungen im Quadratgitter mittels funktionaler Renormierungsgruppe

Julian Lichtenstein

In this thesis a novel computational approach for functional Renormalization Group (fRG) investigations regarding interacting fermions on two-dimensional lattices is derived. The approach is based on the exchange-parametrization fRG [C. Husemann and M. Salmhofer. Phys. Rev. B, 79:195125.] concerning the two-fermion interaction, with additional insertions of truncated partitions of unity that are inspired by the singular-mode fRG [W.-S. Wang, Y.-Y. Xiang, Q.-H. Wang, et al.. Phys. Rev. B, 85:035414.]. These insertions decouple the fermionic propagators from the exchange propagators and thereby lead to a separation of the underlying equations. It is argued that this separation is numerically advantageous and may pave the way for refined, large-scale computational fRG investigations. Furthermore, on the basis of speedup data gained from an implementation of the novel scheme, it is shown that the new equation structure facilitates efficient calculations on a large number of multi-core CPUs. Utilizing the methodical development, two applications are presented afterwards: Firstly, the scheme is applied to the t-t' Hubbard model on a square lattice. In order to test the method, the convergence of the results with respect to increasing truncation length of the partition of unity is analyzed and a comparison to findings from previous fRG studies is drawn. The test yields a fast convergence in most parts of the investigated parameter range. Moreover, it was found that the older findings are approximately reproduced using a short truncation length, while quantitative corrections to the previous results are obtained using longer truncation lengths. In addition to these method focused investigations, the high momentum-space resolution of the implementation was utilized to study ordering vectors of antiferromagnetic phases. A comparison to calculations solely based on the magnetic channel revealed that the inter-channel feedback, as contained in the fRG, generates support for commensurate antiferromagnetic orderings. The second application addresses a modified version of the previous model, in which a Coulomb-like long-range interaction term is added to the local Hubbard interaction. In this work a solution is presented on how the long-range interaction can be implemented in a momentum-space fRG scheme without encountering singularities. Afterwards, phase diagrams are given that compare the results of calculations using short- and long-ranged interactions, showing significantly lower critical scales in the long-range scenario. Finally, screening lengths are extracted from the fRG outcome and are compared to those calculated in a 'random phase approximation'. The comparison reveals quantitative differences between both values. However, the results indicate that the charge screening is not changed qualitatively by the feedback from other channels, i.e., at van Hove filling the screening length tends to zero in both cases.

•Jan 1, 2018•3 citations
We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this method to the Hubbard model on a square lattice using both zero- and finite- temperature methods. Truncating the effective action at the sixth term in fermionic variables we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability Tc^{RG} as function of doping. We calculate furthermore the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type d while the AF fluctuations are of the type s Following the strength of both SC and AF fluctuation along the instability line we obtain the phase diagram. The temperature Tc^{RG} can be identified with the crossover temperature T{co} found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime Tc^{RG} corresponds to the superconducting critical temperature.
We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in the form of the Polchinski equation. The advantage of this renormalization scheme is that the flow itself has a physical interpretation, i.e., the cutoff has the meaning of the temperature. We apply this method to the Hubbard model on a square lattice using both zero- and finite-temperature methods. Truncating the effective action at the sixth term in fermionic variables and neglecting self-energy renormalization, we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability TcRG{T}_{c}^{\mathrm{RG}}TcRG​ as a function of doping. Furthermore we calculate the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type ${d}_{{x}^{2}\ensuremath{-}{y}^{2}},$ while the AF fluctuations are of the type s. Following the strength of both SC and AF fluctuations along the instability line, we obtain the phase diagram. The temperature TcRG{T}_{c}^{\mathrm{RG}}TcRG​ can be identified with the crossover temperature Tco{T}_{\mathrm{co}}Tco​ found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime TcRG{T}_{c}^{\mathrm{RG}}TcRG​ corresponds to the superconducting critical temperature.
In this thesis a novel computational approach for functional Renormalization Group (fRG) investigations regarding interacting fermions on two-dimensional lattices is derived. The approach is based on the exchange-parametrization fRG [C. Husemann and M. Salmhofer. Phys. Rev. B, 79:195125.] concerning the two-fermion interaction, with additional insertions of truncated partitions of unity that are inspired by the singular-mode fRG [W.-S. Wang, Y.-Y. Xiang, Q.-H. Wang, et al.. Phys. Rev. B, 85:035414.]. These insertions decouple the fermionic propagators from the exchange propagators and thereby lead to a separation of the underlying equations. It is argued that this separation is numerically advantageous and may pave the way for refined, large-scale computational fRG investigations. Furthermore, on the basis of speedup data gained from an implementation of the novel scheme, it is shown that the new equation structure facilitates efficient calculations on a large number of multi-core CPUs. Utilizing the methodical development, two applications are presented afterwards: Firstly, the scheme is applied to the t-t' Hubbard model on a square lattice. In order to test the method, the convergence of the results with respect to increasing truncation length of the partition of unity is analyzed and a comparison to findings from previous fRG studies is drawn. The test yields a fast convergence in most parts of the investigated parameter range. Moreover, it was found that the older findings are approximately reproduced using a short truncation length, while quantitative corrections to the previous results are obtained using longer truncation lengths. In addition to these method focused investigations, the high momentum-space resolution of the implementation was utilized to study ordering vectors of antiferromagnetic phases. A comparison to calculations solely based on the magnetic channel revealed that the inter-channel feedback, as contained in the fRG, generates support for commensurate antiferromagnetic orderings. The second application addresses a modified version of the previous model, in which a Coulomb-like long-range interaction term is added to the local Hubbard interaction. In this work a solution is presented on how the long-range interaction can be implemented in a momentum-space fRG scheme without encountering singularities. Afterwards, phase diagrams are given that compare the results of calculations using short- and long-ranged interactions, showing significantly lower critical scales in the long-range scenario. Finally, screening lengths are extracted from the fRG outcome and are compared to those calculated in a 'random phase approximation'. The comparison reveals quantitative differences between both values. However, the results indicate that the charge screening is not changed qualitatively by the feedback from other channels, i.e., at van Hove filling the screening length tends to zero in both cases.