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Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
Strongly Correlated Electrons · Submitted 19 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The asymptotic low $\omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states.
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The abstract, sentence by sentence
We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities. The analysis applies also to SU($M$) magnets with random exchange at large $M$. The spectral densities are computed by numerical analysis of the saddle point equations on the real frequency ($\omega$) axis at zero temperature ($T$). The asymptotic low $\omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU($M$) magnets at low $\omega$ and $T$: this includes a contribution from the time reparameterization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t$-$J$ model in a companion paper.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities. | contribution 1.00 | 0.95 | 0.07 | asserted 0.88 |
| s1 | The analysis applies also to SU($M$) magnets with random exchange at large $M$. | contribution 0.51 | 0.33 | 0.03 | asserted 0.98 |
| s2 | The spectral densities are computed by numerical analysis of the saddle point equations on the real frequency ($\omega$) axis at zero temperature ($T$). | method 1.00 | 0.95 | 0.05 | asserted 1.00 |
| s3 | The asymptotic low $\omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. | result 0.86 | 0.94 | 0.40 | asserted 1.00 |
| s4 | Of possible experimental interest is our computation of the universal spin spectral weight of the SU($M$) magnets at low $\omega$ and $T$: this includes a contribution from the time reparameterization mode, which is the boundary graviton of the holographic dual. | result 0.65 | 0.93 | 0.15 | hedged possibility 0.62 |
| s5 | This analysis is extended to a random $t$-$J$ model in a companion paper. | future work 0.93 | 0.36 | 0.02 | asserted 0.99 |
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The paper
Original abstract
We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities. The analysis applies also to SU($M$) magnets with random exchange at large $M$. The spectral densities are computed by numerical analysis of the saddle point equations on the real frequency ($\omega$) axis at zero temperature ($T$). The asymptotic low $\omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU($M$) magnets at low $\omega$ and $T$: this includes a contribution from the time reparameterization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t$-$J$ model in a companion paper.
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References
How the literature uses it
15 arXiv papers cite this in 65 sentences
Papers citing it · 43 sentences without a confident label
Builds on it 1 paper
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The linear order zero-temperature correction [ref] was generalized to finite temperature in [ref] .
Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models · Corrections to Conformality · 0.89
Uses its method or tool 2 papers
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The coefficients $a_hh'$, $a_hh'h”$ can be calculated using the recursion procedure described in [ref] .
Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models · Corrections to Conformality · 0.84
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At zero temperature, we can readily Fourier transform to position space, similarly to [ref] , which yields: [equation] where $𝐋_ν(x)$ and $I_ν(x)$ are the modified Struve and Bessel functions, respectively, and we have dropped contact terms.
The quantum $p$-spin glass model: A user manual for holographers · Properties of the approximate solution · 0.88
Compares with it 3 papers
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We note that the presence of the mode with $h_1 < 2$ is a new feature of the doped $t$-$J$ model, and was not present in the undoped antiferromagnet examined earlier [ref] ; the leading irrelevant operator in the latter case was the $h_0=2$ boundary graviton.
Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models · Introduction · 0.94
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With this simplification, the resulting integral Bethe-Salpeter equation turns out to act only on frequency space; indeed, it is identical in form to the equations obtained for the SYK model [ref] .
Large $N$ theory of critical Fermi surfaces · Antipodal patch theory and fermion bilinear operators · 0.93
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For the second and third order corrections due to the $h_0 =2$ mode we find: [equation] For $p=3$ this yields $α_0,2 = 25/36$, $α_0,3 = -55/9$ and so on.[ For $p=4$, we get $α_0,2 = 9/4$, $α_0,3 = - 65/4$, which is consistent with [ref] .
The quantum $p$-spin glass model: A user manual for holographers · Conformal perturbation theory · 0.90
Cites it as background 3 papers
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The complex SYK model describes $N≫1$ complex fermions with random interactions [ref] .
Pole-skipping points in 2D gravity and SYK model · Pole-skipping in complex SYK model · 1.00
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In principle one can continue in this fashion and formulate a systematic resonance theory, which has been developed in great generality [ref] .
The quantum $p$-spin glass model: A user manual for holographers · Conformal perturbation theory · 0.84
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Our results are relevant also in the context of the non-Fermi liquid quantum critical point separating a metallic spin-glass phase and a Fermi liquid metal in doped SYK models, which has attracted a lot of attention recently [ref] .
Skewed Non-Fermi Liquids and the Seebeck Effect · Summary and Discussion · 0.88
What it cites · 65 sentences without a confident label
Builds on 2 papers
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In [ref] , the theory was further extended to the $t$-$J$ model, a couple system of both fermions and bosons, and the scaling function $ℱ_h$ was obtained for generic temperature and $U(1)$ charge.
Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode · Kitaev-Suh resonance theory · 0.80
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Finally, we note that we have extended the analyses of the present paper to the doped magnet, described by the SU($M$) $t$-$J$ model studied in Ref. [ref] .
Deconfined critical point in a doped random quantum Heisenberg magnet · Conclusions · 0.99
Uses the method or tool of 7 papers
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Following [ref] we obtain [equation] where the sum goes over all resonances $h_*$ which are the solutions of ([ref]).
Notes on the complex Sachdev-Ye-Kitaev model · Linear order correction · 0.86
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Following [ref] we obtain [equation] where the sum goes over all resonances $h_*$ which are the solutions of ([ref]).
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual · Linear order correction · 0.86
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We find [ref] [equation] The one-point functions in thermal CFT are not necessarily zero and from the scale symmetry we have [ref] [equation] To find constants $b_h$ we consider thermal conformal two point function [equation] Expanding it in series for $τ→0$ we obtain [equation] On the other hand using OPE in ([ref]) we find [equation] where we assumed that the two-point functions of $O_h$ are normalized as in ([ref]).
F-Theorem without Supersymmetry · Free energy from conformal perturbations · 0.93
Uses data or values from 2 papers
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The next order $h(τ)$ was found in [ref] and reads [equation] where $ℓ(x) = g(x) -e^-g(x)Li_2(1-e^g(x))$.
On large $q$ expansion in the Sachdev-Ye-Kitaev model · Large $q$ two point function in the fermionic SYK model · 0.81
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For $q=2$ the exact result for the two point function for $τ>0$ at zero temperature is [ref] : [equation] where $I_1(x)$ and $L_1(x)$ are modified Bessel and Struve functions.
Comments on the Sachdev-Ye-Kitaev model · Two point function for $q=2$ in the fermionic SYK model · 0.81
Compares with 5 papers
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The first term is proportional to $N(βJ)$ and represents correction to the ground energy, whereas the second term is finite and gives contribution to the free energy of order $1/(βJ)^2h-2$, so we find [equation] For $h_0=2$ this result gives $βδ^2 F_h_0 = N 2π^2 q α_S α_0/(βJ)^2$, which exactly agrees with $N/(βJ)^2$ correction computed in [ref] using careful analysis of $h_0=2$ mode [In [ref] it was shown that $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N4π^2α_S/β^3J$ rather than $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N/|τ_12|^4$.
Comments on the Sachdev-Ye-Kitaev model · Free energy from conformal perturbations · 0.95
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The first term is proportional to $N(βJ)$ and represents correction to the ground energy, whereas the second term is finite and gives contribution to the free energy of order $1/(βJ)^2h-2$, so we find [equation] For $h_0=2$ this result gives $βδ^2 F_h_0 = N 2π^2 q α_S α_0/(βJ)^2$, which exactly agrees with $N/(βJ)^2$ correction computed in [ref] using careful analysis of $h_0=2$ mode [In [ref] it was shown that $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N4π^2α_S/β^3J$ rather than $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N/|τ_12|^4$.
Black Holes and Random Matrices · Free energy from conformal perturbations · 0.95
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The first term is proportional to $N(βJ)$ and represents correction to the ground energy, whereas the second term is finite and gives contribution to the free energy of order $1/(βJ)^2h-2$, so we find [equation] For $h_0=2$ this result gives $βδ^2 F_h_0 = N 2π^2 q α_S α_0/(βJ)^2$, which exactly agrees with $N/(βJ)^2$ correction computed in [ref] using careful analysis of $h_0=2$ mode [In [ref] it was shown that $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N4π^2α_S/β^3J$ rather than $⟨O_h_0(τ_1)O_h_0(τ_2)⟩= N/|τ_12|^4$.
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual · Free energy from conformal perturbations · 0.95
Cites as background 16 papers
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We summarize previous works on linear order resonance theory [ref] .
Notes on the complex Sachdev-Ye-Kitaev model · Linear order correction · 0.98
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We summarize previous works on linear order resonance theory [ref] .
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual · Linear order correction · 0.98
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We summarize previous works on linear order resonance theory [ref] .
Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode · Linear order correction · 0.98
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