Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1908.11351 · Physical Review Letters

Sachdev-Ye-Kitaev Non-Fermi-Liquid Correlations in Nanoscopic Quantum Transport

Alexander Altland, Dmitry Bagrets, Alex Kamenev

Published Nov 26, 2019• 55 citations
arXivHTMLPDF

Abstract

Electronic transport in nanostructures, such as long molecules or 2D exfoliated flakes, often goes through a nearly degenerate set of single-particle orbitals. Here we show that in such cases a conspiracy of the narrow band and strong e-e interactions may stabilize a non-Fermi-liquid phase in the universality class of the complex Sachdev-Ye-Kitaev (SYK) model. Focusing on signatures in quantum transport, we demonstrate the existence of anomalous power laws in the temperature dependent conductance, including algebraic scaling T^{3/2} in the inelastic cotunneling channel, separated from the conventional Fermi liquid T^{2} scaling via a quantum phase transition. The relatively robust conditions under which these results are obtained indicate that the SYK non-Fermi-liquid universality class might not be as exotic as previously thought.

DOI
10.1103/physrevlett.123.226801

Related papers

Higher-dimensional Sachdev-Ye-Kitaev non-Fermi liquids at Lifshitz transitions

Arijit Haldar, Sumilan Banerjee, Vijay B. Shenoy

Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.

arXiv:1710.00842•Physical review. B./Physical review. B•Jun 14, 2018•55 citations

Charge transport in graphene-based mesoscopic realizations of Sachdev-Ye-Kitaev models

Oguzhan Can, Emilian M. Nica, Marcel Franz

We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio $p$ between the number of transverse modes in the lead $M$ and the number of the fermion degrees of freedom $N$ on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct $\sqrt{p}$ and $1/\sqrt{p}$ dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias $U$. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to $1/\sqrt{T}$ for bias energy $eU$ smaller than temperature scale ${k}_{B}T$. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.

arXiv:1808.06584•Physical review. B./Physical review. B•Jan 14, 2019•34 citations

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

Debanjan Chowdhury, Antoine Georges, Olivier Parcollet +1 more

We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large $N$ theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.

arXiv:2109.05037•Sep 10, 2021•14 citations

Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model

N. V. Gnezdilov, Jimmy A. Hutasoit, C. W. J. Beenakker

The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated metal with all-to-all random interactions (average strength $J$) between $N$ fermions (complex Dirac fermions or real Majorana fermions). In the large-$N$ limit a conformal symmetry emerges that renders the model exactly soluble. Here we study how the non-Fermi-liquid behavior of the closed system in equilibrium manifests itself in an open system out of equilibrium. We calculate the current-voltage characteristic of a quantum dot, described by the complex-valued SYK model, coupled to a voltage source via a single-channel metallic lead (coupling strength $\mathrm{\ensuremath{\Gamma}}$). A one-parameter scaling law appears in the large-$N$ conformal regime, where the differential conductance $G=dI/dV$ depends on the applied voltage only through the dimensionless combination $\ensuremath{\xi}=eVJ/{\mathrm{\ensuremath{\Gamma}}}^{2}$. Low and high voltages are related by the duality $G(\ensuremath{\xi})=G(\ensuremath{\pi}/\ensuremath{\xi})$. This provides for an unambiguous signature of the conformal symmetry in tunneling spectroscopy.

arXiv:1807.09099•Physical review. B./Physical review. B•Aug 31, 2018•33 citations

Quantum tunneling dynamics in complex SYK model quenched-coupled to a cool-bath

Yevheniia Cheipesh, Andrei I. Pavlov, V. Ohanesjan +2 more

The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the complex-valued SYK model at temperature $T$ coupled to a zero temperature reservoir by a quench. We find out that the tunneling current dynamics reveals a way to distinguish the SYK non-Fermi liquid (nFL) initial state of the subsystem from the disordered Fermi liquid. Temperature dependent contribution to the current's half-life scales linearly in $T$ at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as $T^2$. This provides a characteristic signature of the SYK non-Fermi liquid in a non-equilibrium measurement.

•Nov 10, 2020•3 citations

Family of Sachdev-Ye-Kitaev models motivated by experimental considerations

Étienne Lantagne-Hurtubise, Chengshu Li, Marcel Franz

Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain assumptions about the underlying physical system that (i) render all bilinear terms small compared to four-fermion interactions and (ii) ensure that the coupling constants are approximately all-to-all and independent random variables. In this work we explore, both analytically and numerically, the family of models that arises when we relax these assumptions in ways motivated by real physical systems. By relaxing (i) and allowing large bilinear terms, we obtain a novel, exactly solvable cousin of the $\mathrm{SYK}$ model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$, scaling of the low-energy spectral density, despite being a noninteracting model. By relaxing (ii), we obtain close relatives of the $\mathrm{SYK}$ model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.

arXiv:1803.07197•Physical review. B./Physical review. B•Jun 14, 2018•26 citations
Electronic transport in nanostructures, such as long molecules or 2D exfoliated flakes, often goes through a nearly degenerate set of single-particle orbitals. Here we show that in such cases a conspiracy of the narrow band and strong e-e interactions may stabilize a non-Fermi-liquid phase in the universality class of the complex Sachdev-Ye-Kitaev (SYK) model. Focusing on signatures in quantum transport, we demonstrate the existence of anomalous power laws in the temperature dependent conductance, including algebraic scaling T^{3/2} in the inelastic cotunneling channel, separated from the conventional Fermi liquid T^{2} scaling via a quantum phase transition. The relatively robust conditions under which these results are obtained indicate that the SYK non-Fermi-liquid universality class might not be as exotic as previously thought.
Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio ppp between the number of transverse modes in the lead MMM and the number of the fermion degrees of freedom NNN on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct p\sqrt{p}p​ and 1/p1/\sqrt{p}1/p​ dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias UUU. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to 1/T1/\sqrt{T}1/T​ for bias energy eUeUeU smaller than temperature scale kBT{k}_{B}TkB​T. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the ttt-JJJ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large NNN theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.
The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated metal with all-to-all random interactions (average strength JJJ) between NNN fermions (complex Dirac fermions or real Majorana fermions). In the large-NNN limit a conformal symmetry emerges that renders the model exactly soluble. Here we study how the non-Fermi-liquid behavior of the closed system in equilibrium manifests itself in an open system out of equilibrium. We calculate the current-voltage characteristic of a quantum dot, described by the complex-valued SYK model, coupled to a voltage source via a single-channel metallic lead (coupling strength $\mathrm{\ensuremath{\Gamma}}$). A one-parameter scaling law appears in the large-NNN conformal regime, where the differential conductance G=dI/dVG=dI/dVG=dI/dV depends on the applied voltage only through the dimensionless combination $\ensuremath{\xi}=eVJ/{\mathrm{\ensuremath{\Gamma}}}^{2}$. Low and high voltages are related by the duality $G(\ensuremath{\xi})=G(\ensuremath{\pi}/\ensuremath{\xi})$. This provides for an unambiguous signature of the conformal symmetry in tunneling spectroscopy.
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the complex-valued SYK model at temperature TTT coupled to a zero temperature reservoir by a quench. We find out that the tunneling current dynamics reveals a way to distinguish the SYK non-Fermi liquid (nFL) initial state of the subsystem from the disordered Fermi liquid. Temperature dependent contribution to the current's half-life scales linearly in TTT at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as T2T^2T2. This provides a characteristic signature of the SYK non-Fermi liquid in a non-equilibrium measurement.
Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain assumptions about the underlying physical system that (i) render all bilinear terms small compared to four-fermion interactions and (ii) ensure that the coupling constants are approximately all-to-all and independent random variables. In this work we explore, both analytically and numerically, the family of models that arises when we relax these assumptions in ways motivated by real physical systems. By relaxing (i) and allowing large bilinear terms, we obtain a novel, exactly solvable cousin of the SYK\mathrm{SYK}SYK model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$, scaling of the low-energy spectral density, despite being a noninteracting model. By relaxing (ii), we obtain close relatives of the SYK\mathrm{SYK}SYK model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.