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

Yevheniia Cheipesh, Andrei I. Pavlov, V. Ohanesjan, Koenraad Schalm, N. V. Gnezdilov

Published Nov 10, 2020• 3 citations
OpenAlex

Abstract

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.

Related papers

Quantum tunneling dynamics in a complex-valued Sachdev-Ye-Kitaev model quench-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 paper we consider the complex-valued SYK model at initial temperature $T$ and chemical potential $\ensuremath{\mu}$ coupled to a large reservoir by a quench at time $t=0$. The reservoir is kept at zero temperature and charge neutrality. We find that the dynamics of the discharging process of the SYK quantum dot reveals a distinctive characteristic of the SYK non-Fermi liquid (nFl) state. In particular, we focus on the tunneling current induced by the quench. We show that the 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 ${T}^{2}$.

arXiv:2011.05238•Physical review. B./Physical review. B•Sep 20, 2021•22 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

Resonant level model coupled to a Sachdev-Ye-Kitaev bath

Anastasia Enckell, Stefan K. Kehrein

We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.

arXiv:2602.13132•Feb 13, 2026•0 citations

Quasiparticle tunneling in two coupled chiral SYK model

Avik Chakraborty, Manavendra Mahato

The chiral SYK model [Lian The chiral SYK model, ] is a 1 + 1 -dimensional generalization of the Sachdev-Ye-Kitaev model with chiral Majorana fermions and homogeneous random interactions. In the large- N limit, the model admits an exact solution of the two-point function due to its scaling symmetry and exhibits a quantized thermal Hall conductance consistent with that of a 2 + 1 -dimensional gapped topological system. We study two chiral SYK systems coupled by a relevant quadratic interaction that explicitly breaks scaling and time-reversal symmetry. Working in the regime of weak intersystem coupling, we solve the Dyson-Schwinger equations perturbatively and obtain analytic expressions for two-point functions at finite temperature. Unlike the coupled SYK model in 0 + 1 dimensions, the 1 + 1 -dimensional chiral system does not develop a mass gap, and no thermal phase transition is observed. We show that the leading correction to the thermodynamic free energy is temperature independent, implying that the entropy density remains identical to that of two uncoupled chiral SYK systems. A real-time analysis of the retarded correlator reveals the emergence of massless collective bosonic modes propagating between the two subsystems at zero temperature, signaling quasiparticle tunneling without gap generation. Our results demonstrate a sharp qualitative distinction between relevant deformations of SYK models in zero and one spatial dimensions and highlight the robustness of gapless chiral edge dynamics against explicit scaling symmetry-breaking interactions.

arXiv:2507.18298•Physical review. D/Physical review. D.•May 8, 2026•0 citations

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

Yiming Chen, Hui Zhai, Pengfei Zhang

The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a $$ \sqrt{T} $$ -dependence at relatively high temperature to a linear T-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

arXiv:1705.09818•Journal of High Energy Physics•Jul 1, 2017•81 citations

Universal quench dynamics of q -fermion Yukawa-Sachdev-Ye-Kitaev models

Haixin Qiu, Stefan K. Kehrein

We study the quantum quench of the Yukawa-Sachdev-Ye-Kitaev model and one of its random hopping extensions with q fermions and one boson. Several equilibrium properties are computed for general q with different parameter scaling within the large- N dynamical mean-field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the random hopping term with constant Yukawa coupling or quenching to different final Yukawa couplings. The postquench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak hopping coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.

arXiv:2505.07971•Physical review. B./Physical review. B•Sep 16, 2025•0 citations
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.
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 paper we consider the complex-valued SYK model at initial temperature TTT and chemical potential $\ensuremath{\mu}$ coupled to a large reservoir by a quench at time t=0t=0t=0. The reservoir is kept at zero temperature and charge neutrality. We find that the dynamics of the discharging process of the SYK quantum dot reveals a distinctive characteristic of the SYK non-Fermi liquid (nFl) state. In particular, we focus on the tunneling current induced by the quench. We show that the 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 T2{T}^{2}T2.
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.
We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.
The chiral SYK model [Lian The chiral SYK model, ] is a 1 + 1 -dimensional generalization of the Sachdev-Ye-Kitaev model with chiral Majorana fermions and homogeneous random interactions. In the large- N limit, the model admits an exact solution of the two-point function due to its scaling symmetry and exhibits a quantized thermal Hall conductance consistent with that of a 2 + 1 -dimensional gapped topological system. We study two chiral SYK systems coupled by a relevant quadratic interaction that explicitly breaks scaling and time-reversal symmetry. Working in the regime of weak intersystem coupling, we solve the Dyson-Schwinger equations perturbatively and obtain analytic expressions for two-point functions at finite temperature. Unlike the coupled SYK model in 0 + 1 dimensions, the 1 + 1 -dimensional chiral system does not develop a mass gap, and no thermal phase transition is observed. We show that the leading correction to the thermodynamic free energy is temperature independent, implying that the entropy density remains identical to that of two uncoupled chiral SYK systems. A real-time analysis of the retarded correlator reveals the emergence of massless collective bosonic modes propagating between the two subsystems at zero temperature, signaling quasiparticle tunneling without gap generation. Our results demonstrate a sharp qualitative distinction between relevant deformations of SYK models in zero and one spatial dimensions and highlight the robustness of gapless chiral edge dynamics against explicit scaling symmetry-breaking interactions.
The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a T \sqrt{T} T​ -dependence at relatively high temperature to a linear T-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.
We study the quantum quench of the Yukawa-Sachdev-Ye-Kitaev model and one of its random hopping extensions with q fermions and one boson. Several equilibrium properties are computed for general q with different parameter scaling within the large- N dynamical mean-field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the random hopping term with constant Yukawa coupling or quenching to different final Yukawa couplings. The postquench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak hopping coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.