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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2511.02039 |
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| _version_ | 1866914379165859840 |
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| author | Mishra, Vibhu |
| author_facet | Mishra, Vibhu |
| contents | We propose a model of metallic critical point which we study at $T=0$ in the large-$N$ limit. We start with two species of fermions $u_i, d_i$, each with $N$ flavors and a gas of matrix bosons $b_{ij}$ with $N^2$ components. The fermions interact with each other via the intermediate boson as $\int b_{ij}^{\dagger} \, u_i^{\dagger}d_j$. The bosons have a bare dispersion $\varepsilon_{\textbf{q}}^b = λ_z |\textbf{q}|^z$ and we study the problem in $d$ spatial dimensions. We show that for $d = z+1,$ the electronic self energy shows marginal Fermi liquid behavior. We first evaluate the fermionic self energy $Σ(iω)$ using the standard approximate boson self energy $Π(\textbf{q}, iν) \propto |ν|/|\textbf{q}|$ and find that $Σ(iω) \sim ω\ln(N/|ω|)$ which shows a much weaker dependence on $N$ when compared with similar results from non-SYK large-$N$ Ising-nematic models. Then we evaluate $Σ(iω)$ again using a more precise form of $Π(\textbf{q}, iν)$ which allows us to study the interplay between $N \rightarrow \infty$ limit for which $Σ(iω) \sim ω\ln(1/|ω|)$, and the $ω\rightarrow 0$ limit where we recover $Σ(iω) \sim ω\ln(N/|ω|)$. We also use the full bosonic self energy to obtain the correction to the bosonic specific heat as $\frac{T}{N} \ln(1/T)$. Since there are $N^2$ bosons and $N$ fermions, the bulk heat capacity for both fermions and bosons shows nearly identical functional form $NVT \ln(N/T)$ and $NVT \ln(1/T)$ respectively for $T \rightarrow 0$. This suggests that coupling the hybridization operator $u^{\dagger}d$ to non-relativistic bosons for $d=3$ and relativistic bosons for $d=2$ provides a simple route to marginal Fermi liquid scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas Mishra, Vibhu Strongly Correlated Electrons We propose a model of metallic critical point which we study at $T=0$ in the large-$N$ limit. We start with two species of fermions $u_i, d_i$, each with $N$ flavors and a gas of matrix bosons $b_{ij}$ with $N^2$ components. The fermions interact with each other via the intermediate boson as $\int b_{ij}^{\dagger} \, u_i^{\dagger}d_j$. The bosons have a bare dispersion $\varepsilon_{\textbf{q}}^b = λ_z |\textbf{q}|^z$ and we study the problem in $d$ spatial dimensions. We show that for $d = z+1,$ the electronic self energy shows marginal Fermi liquid behavior. We first evaluate the fermionic self energy $Σ(iω)$ using the standard approximate boson self energy $Π(\textbf{q}, iν) \propto |ν|/|\textbf{q}|$ and find that $Σ(iω) \sim ω\ln(N/|ω|)$ which shows a much weaker dependence on $N$ when compared with similar results from non-SYK large-$N$ Ising-nematic models. Then we evaluate $Σ(iω)$ again using a more precise form of $Π(\textbf{q}, iν)$ which allows us to study the interplay between $N \rightarrow \infty$ limit for which $Σ(iω) \sim ω\ln(1/|ω|)$, and the $ω\rightarrow 0$ limit where we recover $Σ(iω) \sim ω\ln(N/|ω|)$. We also use the full bosonic self energy to obtain the correction to the bosonic specific heat as $\frac{T}{N} \ln(1/T)$. Since there are $N^2$ bosons and $N$ fermions, the bulk heat capacity for both fermions and bosons shows nearly identical functional form $NVT \ln(N/T)$ and $NVT \ln(1/T)$ respectively for $T \rightarrow 0$. This suggests that coupling the hybridization operator $u^{\dagger}d$ to non-relativistic bosons for $d=3$ and relativistic bosons for $d=2$ provides a simple route to marginal Fermi liquid scaling. |
| title | Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.02039 |