Quantum phase transition in the Yukawa-SYK model

Wang, Yuxuan; Chubukov, Andrey V.

doi:10.1103/physrevresearch.2.033084

Cited by 48 publications

(41 citation statements)

References 75 publications

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“…In (1.2) the U(1) is the usual charge symmetry, while the enhanced SU(2) symmetry models the physical spin; we may think of σ as labeling the two spin states, up and down. We note that some results on spontaneous U(1) symmetry breaking in models with random couplings have already appeared in the literature [30][31][32][33][34][35][36][37]. For example, toy models of superconductivity introduced in [31,32,37] include random Yukawa interactions of fermion-phonon type.…”

Section: Introductionmentioning

confidence: 78%

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

Klebanov

Milekhin

Tarnopolsky

et al. 2020

J. High Energ. Phys.

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As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) × U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator $$ {c}_{1i}^{\dagger }{c}_{2i} $$ c 1 i † c 2 i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N.

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Section: Introductionmentioning

confidence: 78%

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

Klebanov

Milekhin

Tarnopolsky

et al. 2020

J. High Energ. Phys.

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“…The particle number n is related to the spectral asymmetry E though the generalized Luttinger theorem 39,40 :…”

Section: Discussionmentioning

confidence: 99%

“…In the SYK literature one frequently uses ∆ = (1 + γ)/4 instead of γ. The spectral asymmetry parameter E can be directly related to the particle density n = c † iσ c iσ via a generalized Luttinger theorem 39,40 , where E(n = 1/2) = 0. It is also linked to the density dependence of the zero-point entropy 41 2πE = ∂S0 ∂n .…”

Section: A Syk-eliashbergmentioning

confidence: 99%

Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals

Inkof,

Schalm,

Schmalian

2021

Preprint

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Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of a gravity theory with emergent space-time from a quantum many-body Hamiltonian -the Yukawa SYK model -where the Eliashberg formalism is exact. Exploiting the power of holography, we then determine the dynamic pairing susceptibility of the model. Our holographic map comes with the potential to use quantum gravity corrections to go beyond the Eliashberg regime.

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“…In this work, we circumvent such difficulty by examining a variant of the Sachdev-Ye-Kitaev (SYK) model [23][24][25][26][27], so called the Yukawa-SYK model [28][29][30][31], which is exactly solvable and supports non-Fermi liquid ground states. While the previously studied models use the fixed variance of the random coupling, we introduce a continuous distribution of variances.…”

Section: Introductionmentioning

confidence: 99%

“…It is important to note that the Yukawa-SYK model is defined by not only the Hamiltonian but also the statistical properties of the random couplings (g ij,k ). Most of previous studies on various families of the SYK model focused on the random couplings with zero mean (g ij,k = 0) and constant variance ((g ij,k ) 2 = λ) [26][27][28][29][30][31][33][34][35][36][37][38]. However, we can also consider the random couplings whose variances obey a well-defined distribution, i.e., (g ij,k ) 2 = λ k has the k dependence such that the set of the variances {λ k } forms a continuous distribution ρ(λ) in the large M limit.…”

Section: Introductionmentioning

confidence: 99%

Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence

Choi,

Tavakol,

Kim

2021

Preprint

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The interplay of non-Fermi liquid and superconductivity born out of strong dynamical interactions is at the heart of the physics of unconventional superconductivity. As a solvable platform of the strongly correlated superconductors, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, which describes spin-1/2 fermions coupled to bosons by the random, all-to-all, spin independent and dependent Yukawa interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow a continuous distribution rather than being fixed to a constant. By tuning the analytic behavior of the distribution, we could control the fermion incoherence to systematically examine various normal states ranging from the Fermi liquid to non-Fermi liquids that are different from the conformal solution of the SYK model with a constant variance. Using the linearized Eliashberg theory, we show that the onset of the unconventional spin triplet pairing is preferred with the spin dependent interactions while all pairing channels show instabilities with the spin independent interactions. Although the interactions strongly damp the fermions in the non-Fermi liquid, the same interactions also dress the bosons to strengthen the tendency to pair the incoherent fermions. As a consequence, the onset temperature Tc of the pairing is enhanced in the non-Fermi liquid compared to the case of the Fermi liquid.

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Quantum phase transition in the Yukawa-SYK model

Cited by 48 publications

References 75 publications

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals

Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence

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