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Vortex Fermi Liquid and Strongly Correlated Quantum Bad Metal
by Nayan MyersonJain, ChaoMing Jian, Cenke Xu
Submission summary
Authors (as registered SciPost users):  ChaoMing Jian 
Submission information  

Preprint Link:  https://arxiv.org/abs/2209.04472v2 (pdf) 
Date submitted:  20220922 18:34 
Submitted by:  Jian, ChaoMing 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
The semiclassical description of twodimensional ($2d$) metals based on the quasiparticle picture suggests that there is a universal threshold of the resistivity: the resistivity of a $2d$ metal is bounded by the so called MottIoffeRegal (MIR) limit, which is at the order of $h/e^2$. If a system remains metallic while its resistivity is beyond the MIR limit, it is referred to as a "bad metal", which challenges our theoretical understanding as the very notion of quasiparticles is invalidated. The description of the system becomes even more challenging when there is also strong correlation between the electrons. Partly motivated by the recent experiment on transition metal dichalcogenides moir\'{e} heterostructure, we seek for understanding of strongly correlated bad metals whose resistivity far exceeds the MIR limit. For some strongly correlated bad metals, though a microscopic description based on electron quasiparticles fails, a tractable dual description based on the "vortex of charge" is still possible. We construct a concrete example of such strongly correlated bad metals where vortices are fermions with a Fermi surface, and we demonstrate that its resistivity can be exceptionally large at zero temperature. And when extra charge $\delta n_e$ is doped into the system away from halffilling, a small Drude weight proportional to $(\delta n_e)^2$ will emerge in the optical conductivity .
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This manuscript deals with a well studied problem in the literature, which the authors acknowledge by citing most important references in the field. Concerning the vortex liquid, the authors also acknowledge that "we are not the first to investigate correlated electrons as vortex liquid". The duality approach employed is also standard. At first sight, the manuscript does not appear as something involving great originality. There are nevertheless a few SciPost criteria of acceptance that may be considered, like for example, "open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work". Before making a final decision, I would like the authors address a few points, which are most likely easy to comment/answer.
1. It seems there is a typo in Eq. (4), the mutual ChernSimons term (with the Kmatrix) has to be divided by $4\pi$ rather than $2\pi$, otherwise the charge will not be $4e$ as stated. As it stands, integrating out $\widetilde{a}_1$ leads to the constraint $\widetilde{a}_2=a$ and we are left with $\frac{2}{2\pi} a\wedge dA^e$.
2. Since the authors don't write the fermionic Lagrangian from Eq. (5) explicitly, it would be useful for the reader if they could provide more information about it. After all the authors integrate out the fermions later on to obtain the effective Lagrangian (which is actually an action) of Eq. (7). Incidentally, why are the authors not writing the momentum dependence of the vacuum polarization at this stage? I understand that the calculation of the conductivity requires letting the momentum vanish, but is there any particular reason why the momentum is not being written? Is it because of the nature of the background field?
3. The authors mention in the conclusion that the partons are confined at higher temperatures, so parton deconfinement is happening as a quantum phase transition at zero temperature. However, there are examples of deconfinement by temperature effects. For instance, quarks deconfine at very high temperatures. An analytically tractable example of deconfinement at finite temperture is Polyakov's compact electrodynamics in 2+1 dimension, where test charges are permanently confined at zero temperature, but deconfine at finite temperature, see for instance the old paper by B Svetitsky, LG Yaffe, at https://doi.org/10.1016/05503213(82)901729 . What is the role of the charge $4e$ in this case? Is this the reason preventing finite temperature deconfinement to happen? In several condensed matter theories the finite temperature deconfinement does not happen because the theory becomes more classical. The authors seem to imply that this is the case, which seems plausible.
Strengths
1 tractable model with clear calculations.
2 addressing the important problem of understanding how bad metal type behavior can arise.
Weaknesses
The below is not a true "weakness" yet an item that the authors might consider. It is a matter of style yet the authors may wish to add some further selfcontained physical background and explanations before briefly citing results of earlier references and jotting down results from these (such as in, e.g., Eq. 4).
Report
This paper is very interesting and I strongly recommend its publication.
Finding a physically appealing tractable model violating the MottIoffeRegel bound is a long standing quest. The main impetus for this problem has been the "bad metal" behavior associated with a violation of this bound at high temperatures. The work by Nayan MyersonJain, ChaoMing Jian, and Cenke Xu makes a notable related advance in illustrating how violations may arise at zero temperature. A main workhorse is a simple analysis of fermionic dual vortices in a parton construction. The reasoning used by the authors is elegant.