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A low-energy effective Hamiltonian for Landau quasiparticles
by Pierre-Louis Taillat, Hadrien Kurkjian
Submission summary
| Authors (as registered SciPost users): | Pierre-Louis Taillat |
| Submission information | |
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| Preprint Link: | scipost_202511_00051v1 (pdf) |
| Date submitted: | Nov. 21, 2025, 11:05 a.m. |
| Submitted by: | Pierre-Louis Taillat |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme relies on an energy cutoff $\Lambda$ which removes the quasi-resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau interaction function $f$ and the collision amplitude in a single amplitude $\mathcal{A}$ regularized by $\Lambda$. Our effective theory captures all the low-energy physics of Fermi fluids that support Landau quasiparticles, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to an atomic Fermi gas with contact interaction to compute the speed of zero sound in function of the scattering length $a$. We also recover the Gork'ov-Melik Barkhudarov correction to the superfluid gap and critical temperature as a direct consequence of the dressing of particles into Landau quasiparticles.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1- it devises a renormalization group like construction of Landau quasi-particles which is explicit at weak interactions
2- many observables, and Bolztmann equations, are computed explicitly
3- relevant for ultracold atomic gas of fermions away from unitarity
Weaknesses
1- it is not always clear what is new and what is just a reframing of old results in a new language
2- it is not always clear what has been computed explicitly and what is taken from some other references
3- many typos and undefined quantities in the equations and text
Report
This manuscript describes a renormalization procedure to construct Landau quasi-particles, which allows for explicit calculations in the weakly interacting regime (attractive or repulsive). Quantities that are usually not included in Landau's theory of Fermi liquid are automatically included . This method allows for deriving Boltzmann equations as well as transport properties. A shorter version of this work has been published recently in PRL, and this manuscript expands on this work to derive additional results.
The manuscript deserves to be published in SciPost Physics once the main weaknesses listed above are addressed :
1- it is not always clear what is new and what is just a reframing of old results in a new language. Of course, the lifetime of quasiparticles, or the correction beyond BCS to T_c, have been known for a long time. But what about the result of Eq. 223, or the transport equations? Which part is brand new, and which is maybe more conveniently obtained with the present approach? The manuscript would be strengthened if this were more explicit.
2- Sometimes, it is not clear if something has been computed explicitly, or could be computed explicitly but has been taken from a different paper. For instance, why display in Fig 4 the result from Ref 46? Couldn't it be computed from the present formalism? If not, why? If yes, why not do it here? Same thing for the contact discussed just after. Other example: are Eq. 213 and 214 derived from the present formalism? And how?
The two points above shows that it would greatly help the reader if a small subsection or table were present at the end of the introduction. It would summarize what is computable with the present approach, or out of reach, and what results obtained here are well known, and which are new. Also, explaining why the present approach is needed to get those new results would help.
3- There are many typos and undefined quantities, see below.
Other remarks: - l212 and following: What is an ergodic eigenstate? The sentence "eigenstates appear as ergodic mixtures of all quasiparticles states, in accordance with ETH" sounds like wishful thinking. Is there any evidence of this scenario? Otherwise, it should be stated as a hypothesis or removed.
-l 218 and below. I do not understand this paragraph. Why should Lambda be tuned to have physical quantities independent of it? By construction, in an exact calculation, the dependence on Lambda of the unitary transformation will disappear from any physical observable, even for stupid choices of Lambda. Of course, some choices (such as the ones advocated in the paper) are better, because they allow for controlling some approximation and do actual calculations.
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l549/550: it is not clear if the replacement of B by A is an approximation or an exact result due to some unexplained properties of A and B.
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I find the subsection on the Born-Markov approximation (p. 22) particularly unclear. Once again, it is not clear whether the contracted terms drop out is an approximation or not. Or do they mean that <a^dag c><b^dag d> = <b^dag c><a^dag d> for some reason unspecified?
Requested changes
Many times, quantities are not defined, or defined much later: - l 165: k_F is not defined in the introduction - Eq. 3: \mathcal{D} is never defined - Eq. 102: \bar{a} is never defined - Eq. 129: H_2 does not seem to be defined anywhere - l1116: the RPA is mentioned for the first time here, shouldn't it be discussed in the corresponding section?
There are also a lot of typos: - l235: defined -> define - Eqs. 74, 75, 78: omega_p becomes epsilon_p and then again omega_p -Eq 118: missing a hat on Q. - l566: no Appendix number is given, and the appendix seems to be missing... without it, the justification of dropping terms in Eq. 123 is missing. - Eq. 124 and l569: Delta t is not defined. Next line, e^(eta t) -> e^(eta t'). The assumption Delta t eta>>1 should be given explicitly. - l745: most of the equation is missing - l853: two \pm are incorrectly placed - l924: it is written u(theta)=cos(theta), then the next sentence says "we assume u(theta) cos(theta)=1", which seems contradictory. -Fig 8 and 9: The legends of those figures mention a tau_sigma, but the caption of Fig 8 only refers to tau, as does the text. - Fig 9 and l945/l955: the figure says omega_0 tau_sigma=450.0, while the text says omega_0 tau=4500.
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