Publisher's Note: Hierarchy of relevant couplings in perturbative renormalization group transformations [Phys. Rev. B<b>81</b>, 121107(R) (2010)]

Shih, Hong-Yan; We, Huang; Hsu, Sze-Bi; Lin, Hsiu-Hau

doi:10.1103/physrevb.81.209901

Phys. Rev. B

2010

DOI: 10.1103/physrevb.81.209901

|View full text |Cite

Publisher's Note: Hierarchy of relevant couplings in perturbative renormalization group transformations [Phys. Rev. B81, 121107(R) (2010)]

Hong-Yan Shih¹,

Huang We²,

Sze-Bi Hsu³

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2012

2023

Publication Types

Select...

Article5

Relationship

Self Cite4

Independent1

Authors

Journals

Cited by 8 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, f ii = 0 and fii = 0 to avoid double counting. By integrating the two sets of RG equations numerically, we found all couplings are well described the scaling ansatz [42],…”

mentioning

confidence: 88%

Anomalous isotope effect in iron-based superconductors

Lin

2019

Sci Rep

Self Cite

View full text Add to dashboard Cite

The role of electron-phonon interactions in iron-based superconductor is currently under debate with conflicting experimental reports on the isotope effect. To address this important issue, we employ the renormalization-group method to investigate the competition between electron-electron and electron-phonon interactions in these materials. The renormalization-group analysis shows that the ground state is a phonon-dressed unconventional superconductor: the dominant electronic interactions account for pairing mechanism while electron-phonon interactions are subdominant. Because of the phonon dressing, the isotope effect of the critical temperature can be normal or reversed, depending on whether the retarded intra- or inter-band interactions are altered upon isotope substitutions. The connection between the anomalous isotope effect and the unconventional pairing symmetry is discussed at the end.

show abstract

“…In addition, f ii = 0 and fii = 0 to avoid double counting. By integrating the two sets of RG equations numerically, we found all couplings are well described the scaling ansatz [42],…”

mentioning

confidence: 88%

Anomalous isotope effect in iron-based superconductors

Lin

2019

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…γi , where l d is the divergent length scale in one-loop RG, the hierarchy of the relevant couplings can be directly read out from the RG exponent γ i [41,42]. Combining with the Abelian bosonization method, the phase diagram of a ladder system is determined [35,38,39].…”

mentioning

confidence: 99%

“…Combining with the Abelian bosonization method, the phase diagram of a ladder system is determined [35,38,39]. Furthermore, the relative values of the charge and spin gaps between different Fermi points can be determined by the RG exponents [41]. This allows us to distinguish the d-wave superconductivity with an anisotopic spin-gap (referred as d-SC 2 here) in a two-leg ladder with heavy doping, n < 0.6.…”

mentioning

confidence: 99%

Possible quantum phase manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms

Irwin

Tsai

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. Different effective interactions and novel correlated quantum many-body phases may be engineered in these systems, with the different phases being tunable via external parameters. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak inter-species interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by to the on-site inter-species interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge density wave instability in the two-leg ladder after the renormalization group transformation. Parameterizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system.

show abstract

“…Besides, as the number of couplings grow, reading out the desired messages from RG flows can be challenging as well. Recently, we found a scaling ansatz [12], characterized by a set of RG exponents, for electron-electron interactions in many correlated systems. These RG exponents build a clear hierarchy of relevant couplings and serve as an unambiguous indicator for the ground-state instabilities.…”

mentioning

confidence: 99%

“…The ground state of the doped two-leg ladder [12,14,22] depends on the filling n, i.e. average number of electrons per lattice site.…”

mentioning

confidence: 99%

Renormalization-group exponents for superconducting phases in two-leg ladders

Cai

We²,

Lin³

2012

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length l d and a set of renormalizationgroup exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, nontrivial constraints among the exponents are derived and explained.PACS numbers: 71.10. Fd, 71.10.Hf, 71.27.+a, 71.10.Pm Even though superconductivity has been observed [1] for one hundred years, the mechanism turning electrons into pairs remains an open question. In conventional superconductors, phonons mediate effective attractions [2] between electron in the low-energy limit and lead to Cooper pair formation near the Fermi surface. On the other hand, for unconventional superconductors[3] like cuprates, phonon-mediated interactions seem to play a secondary role while the electronic correlations are believed to reigns. It is speculated that the spin fluctuations is the key to the pairing mechanism (and perhaps the pairing symmetry as well). However, it hasn't been fully understood how Coulomb repulsion eventually glues electrons into pairs.The discovery of iron-based superconductors keeps the puzzling charm going. Collecting from experimental observations, it is believed that electronic correlations in these materials are important but much weaker than those in cuprates. Though the renormalization-group (RG) analysis[4-6] for electron-electron interactions delivers the correct pairing symmetry, the isotope effects measured in laboratories show conflicting results. In addition, the iron-based superconductors are distinct from the cuprates due to the presence of multiple active bands.Inspired by the anomalous isotope effects in iron-based superconductors, it is helpful to investigate the competitions between electron-electron [7,8] and electron-phonon interactions [9][10][11] by RG analysis. The major difficulty lies in the enormous couplings for all allowed interactions. Besides, as the number of couplings grow, reading out the desired messages from RG flows can be challenging as well. Recently, we found a scaling ansatz [12], characterized by a set of RG exponents, for electron-electron interactions in many correlated systems. These RG exponents build a clear hierarchy of relevant couplings and serve as an unambiguous indicator for the ground-state instabilities. We are curious whether similar scaling ansatz exists even when the retarded interactions mediated by phonons are included.In this Rapid Communications, we show that the scaling ansatz works in the presence of both electron-electron and electron-phonon interactions and the patterns of the extracted RG exponents describe the ground states and also the quantum phase transitions between them. To make the discussions concrete, we study the exemplar two-leg ladder shown in Fig....

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Publisher's Note: Hierarchy of relevant couplings in perturbative renormalization group transformations [Phys. Rev. B81, 121107(R) (2010)]

Cited by 8 publications

References 0 publications

Anomalous isotope effect in iron-based superconductors

Anomalous isotope effect in iron-based superconductors

Possible quantum phase manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms

Renormalization-group exponents for superconducting phases in two-leg ladders

Contact Info

Product

Resources

About