Particle-Hole Symmetry of Charge Excitation Spectra in the Paramagnetic Phase of the Hubbard Model

Dao, Vu Hung; Frésard, Raymond

doi:10.12693/aphyspola.133.336

Cited by 3 publications

(3 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These two fields are at the first place associated with charge fluctuations, and one might wonder whether the charge fluctuation spectrum depends on this asymmetry, but it could be shown that this is not the case, at least when it is computed to one-loop order around the paramagnetic saddle-point. [67,87] In this context this one-loop calculation was believed to coincide with the time-dependent Gutzwiller approximation until discrepancies between the two were put forward. [67] This motivated an extension of it to achieve agreement with the slave boson one-loop calculation.…”

Section: Introductionmentioning

confidence: 99%

Exact Functional Integration of Radial and Complex Slave‐Boson Fields: Thermodynamics and Dynamics of the Two‐Site Extended Hubbard Model

Dao,

Frésard

2024

Annalen der Physik

Self Cite

View full text Add to dashboard Cite

The functional integral formulation of the Hubbard model when treated in its Kotliar‐Ruckenstein representation in the radial gauge involves fermionic, as well as complex and radial slave boson fields. In order to improve on the understanding of the interplay of the three types of fields, and on the nature of the latter, a comprehensive investigation of an exactly solvable two‐site cluster is performed, as it entails all pitfalls embodied in this approach. It is first shown that the exact partition function is recovered, even when incorporating in the calculation the square root factors that are at the heart of the representation, when suitably regularized. It is shown that using radial slave boson fields allows to overcome all hurdles following from the normal ordering procedure. It is then demonstrated that this applies to the Green's function as well, and to the correlation functions of physical interest, thereby answering the criticisms raised by Schönhammer [K. Schönhammer, Phys. Rev. B 1990 42, 2591]. In addition, the investigation generalizes the calculations to the Hubbard model extended by a non‐local Coulomb interaction.

show abstract

Section: Introductionmentioning

confidence: 99%

Exact Functional Integration of Radial and Complex Slave‐Boson Fields: Thermodynamics and Dynamics of the Two‐Site Extended Hubbard Model

Dao,

Frésard

2024

Annalen der Physik

Self Cite

View full text Add to dashboard Cite

show abstract

“…These fields are primarily associated with charge fluctuations, and one might wonder about the consequences of this asymmetry on the charge fluctuation spectrum. It turns out that the latter is independent of the choice, at least when computed to one-loop order around the paramagnetic saddle-point [35,36].…”

Section: Introductionmentioning

confidence: 99%

“…It may be chosen to be the d field, which accounts for doubly occupied sites, or the e field, which accounts for empty sites. These two fields are at the first place associated with charge fluctuations, and one might wonder whether the charge fluctuation spectrum depends on this asymmetry, but it could be shown that this is not the case, at least when it is computed to one-loop order around the paramagnetic saddle-point [67,87]. In this context this one-loop calculation was believed to coincide with the time-dependent Gutzwiller approximation (TDGA) until discrepancies between the two were put forward [67].…”

Section: Introductionmentioning

confidence: 99%

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

Dao

Frésard

2019

Annalen der Physik

Self Cite

View full text Add to dashboard Cite

The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle-point approximation is performed. Within the Kotliar-Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, we present the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.

show abstract

Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

Dao¹,

Frésard²

2017

EPL

Self Cite

View full text Add to dashboard Cite

Fd -Lattice fermion models PACS 72.15.Nj -Collective modes PACS 71.30.+h -Metal-insulator transitions and other electronic transitionsAbstract -The charge dynamical response function of the t−t ′ −U Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slighty affects the renormalisation of the quasiparticle mass. In contrast a negative t ′ /t notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density n 0.5 (n 1.5) we found that it enhances (reduces) the damping of the zero-sound mode. Furthermore it softens (hardens) the upper-Hubbard-band collective mode at positive (negative) doping. Our results are compared to existing numerical simulations.

show abstract

Particle-Hole Symmetry of Charge Excitation Spectra in the Paramagnetic Phase of the Hubbard Model

Cited by 3 publications

References 79 publications

Exact Functional Integration of Radial and Complex Slave‐Boson Fields: Thermodynamics and Dynamics of the Two‐Site Extended Hubbard Model

Exact Functional Integration of Radial and Complex Slave‐Boson Fields: Thermodynamics and Dynamics of the Two‐Site Extended Hubbard Model

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

Contact Info

Product

Resources

About