Solvable Strong-Coupling Quantum-Dot Model with a Non-Fermi-Liquid Pairing Transition

Wang, Yuxuan

doi:10.1103/physrevlett.124.017002

Cited by 77 publications

(79 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…44 for arbitrary γ. A similar result has been recently found in the study of the pairing in the SYK-type model [74][75][76] (see the article by Daniel Hauck, Markus Klug, Ilya Esterlis, and Jörg Schmalian for this issue).…”

Section: N < Ncrsupporting

confidence: 83%

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

et al. 2020

Self Cite

View full text Add to dashboard Cite

Near a quantum-critical point, a metal reveals two competing tendencies: destruction of fermionic coherence and attraction in one or more pairing channels. We analyze the competition within Eliashberg theory for a class of quantum-critical models with an effective dynamical electron-electron interaction V (Ωm) ∝ 1/|Ωm| γ (the γ-model) for 0 < γ < 1. We argue that the two tendencies are comparable in strength, yet the one towards pairing is stronger, and the ground state is a superconductor. We show, however, that there exist two distinct regimes of system behavior below the onset temperature of the pairing Tp. In the range Tcross < T < Tp fermions remain incoherent and the spectral function A(k, ω) and the density of states N (ω) both display "gap filling" behavior in which, e.g., the position of the maximum in N (ω) is set by temperature rather than the pairing gap. At lower T < Tcross, fermions acquire coherence, and A(k, ω) and N (ω) display conventional "gap closing" behavior, when the peak position in N (ω) scales with the gap and shifts to a smaller value as T increases. We argue that the existence of the two regimes comes about because of special behavior of fermions with frequencies ω = ±πT along the Matsubara axis. Specifically, for these fermions, the component of the self-energy, which competes with the pairing, vanishes in the normal state. We further argue that the crossover at T ∼ Tcross comes about because Eliashberg equations allow an infinite number of topologically distinct solutions for the onset temperature of the pairing within the same gap symmetry. Only one solution, with the highest Tp, actually emerges, but other solutions are generated and modify the form of the gap function at T ≤ Tcross. Finally, we argue that the actual Tc is comparable to Tcross, while at Tcross < T < Tp phase fluctuations destroy superconducting long-range order, and the system displays a pseudogap behavior.

show abstract

Section: N < Ncrsupporting

confidence: 83%

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…We assume ω 0 to be positive. We have chosen the Yukawa coupling to be imaginary, such that the effective interaction in the Cooper channel is repulsive [39,40]. The model has an exact particle-hole symmetry, under which μ → −μ.…”

Section: The Modelmentioning

confidence: 99%

“…In this communication, we consider the generalization of the SYK model, the Yukawa-SYK (Y-SYK) model [39][40][41], in which M flavors of dispersion-less fermions in a quantum dot randomly interact with N flavors of massive bosons, e.g., optical phonons or gapped collective spin or charge fluctuations. The interest to this model has been triggered by its rich and unconventional physics, and by recent experimental discoveries of strongly correlated behavior in flat band systems like magic angle twisted bilayer graphene [42,43] and d xy band in Fe-based superconductors [44].…”

Section: Introductionmentioning

confidence: 99%

“…The interest to this model has been triggered by its rich and unconventional physics, and by recent experimental discoveries of strongly correlated behavior in flat band systems like magic angle twisted bilayer graphene [42,43] and d xy band in Fe-based superconductors [44]. The Y-SYK model has been earlier studied at half-filling [39,40,45]. It was shown that the interaction "self-tunes" the system into a NFL, quantum-critical (QC) regime, despite that a bare bosonic mass is finite.This QC regime may in turn become unstable towards non-BCS superconductivity [39][40][41][46][47][48][49]28,50,51].…”

Section: Introductionmentioning

confidence: 99%

“…The Y-SYK model has been earlier studied at half-filling [39,40,45]. It was shown that the interaction "self-tunes" the system into a NFL, quantum-critical (QC) regime, despite that a bare bosonic mass is finite.This QC regime may in turn become unstable towards non-BCS superconductivity [39][40][41][46][47][48][49]28,50,51]. Like the SYK model, the Y-SYK model also saturates the upper bound for the onset rate of quantum chaos [52], indicating the existence a classical holographic dual.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum phase transition in the Yukawa-SYK model

Wang

Chubukov

2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

We study the quantum phase transition upon varying the fermionic density ν in a solvable model with random Yukawa interactions between N bosons and M fermions, dubbed the Yukawa-SYK model. We show that there are two distinct phases in the model: an incompressible state with gapped excitations and an exotic quantumcritical, non-Fermi liquid state with exponents varying with ν. We show analytically and numerically that the quantum phase transition between these two states is first-order, as for some range of ν the NFL state has a negative compressibility. In the limit N/M → ∞, the first-order transition gets weaker and asymptotically becomes second-order, with an exotic quantum-critical behavior. We show that fermions and bosons display highly unconventional spectral behavior in the transition region.

show abstract

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

Klebanov

Milekhin

Tarnopolsky

et al. 2020

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Solvable Strong-Coupling Quantum-Dot Model with a Non-Fermi-Liquid Pairing Transition

Cited by 77 publications

References 73 publications

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

Quantum phase transition in the Yukawa-SYK model

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

Contact Info

Product

Resources

About