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:1906.03265 · Physical Review Letters

Theory of a Planckian Metal

Aavishkar A. Patel, Subir Sachdev A

Published Aug 7, 2019• 137 citations
arXivHTMLPDF

Abstract

We present a lattice model of fermions with N flavors and random interactions that describes a Planckian metal at low temperatures T→0 in the solvable limit of large N. We begin with quasiparticles around a Fermi surface with effective mass m^{*} and then include random interactions that lead to fermion spectral functions with frequency scaling with k_{B}T/ℏ. The resistivity ρ obeys the Drude formula ρ=m^{*}/(ne^{2}τ_{tr}), where n is the density of fermions, and the transport scattering rate is 1/τ_{tr}=fk_{B}T/ℏ; we find f of order unity and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes nonresonant in the bare quasiparticle energies only renormalize m^{*}, while resonant processes are shown to produce the Planckian behavior.

DOI
10.1103/physrevlett.123.066601

Related papers

Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions

Peter Cha, Nils Wentzell, Olivier Parcollet +2 more

"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

arXiv:2002.07181•Proceedings of the National Academy of Sciences•Jul 22, 2020•72 citations

Conductivity in a Honeycomb Sachdev-Ye-Kitaev Lattice

Koushik Swaminathan

Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.

•Oct 31, 2019•0 citations

Universal theory of strange metals from spatially random interactions

Aavishkar A. Patel, Haoyu Guo, Ilya Esterlis +1 more

Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.

arXiv:2203.04990•Science•Aug 17, 2023•115 citations

Strange Metals and Planckian Transport in a Gapless Phase from Spatially Random Interactions

Aavishkar A. Patel, Peter Lunts, Michael S. Albergo

“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ( T ) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large- N limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in- T resistivity with a universal “Planckian” transport scattering rate Γ tr ∼ k B T / ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.

arXiv:2410.05365•Physical Review X•Aug 19, 2025•9 citations

Planckian metal at a doping-induced quantum critical point

Philipp T. Dumitrescu, Nils Wentzell, Antoine Georges +1 more

We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by $T$-linear Planckian behavior, $\ensuremath{\omega}/T$ scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The $\ensuremath{\omega}/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a ``skewed'' non-Fermi liquid.

arXiv:2103.08607•Physical review. B./Physical review. B•May 6, 2022•23 citations

Magnetotransport in a Model of a Disordered Strange Metal

Aavishkar A. Patel, John McGreevy, Daniel P. Arovas +1 more

Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

arXiv:1712.05026•Physical Review X•May 22, 2018•128 citations
We present a lattice model of fermions with N flavors and random interactions that describes a Planckian metal at low temperatures T→0 in the solvable limit of large N. We begin with quasiparticles around a Fermi surface with effective mass m^{} and then include random interactions that lead to fermion spectral functions with frequency scaling with k_{B}T/ℏ. The resistivity ρ obeys the Drude formula ρ=m^{}/(ne^{2}τ_{tr}), where n is the density of fermions, and the transport scattering rate is 1/τ_{tr}=fk_{B}T/ℏ; we find f of order unity and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes nonresonant in the bare quasiparticle energies only renormalize m^{*}, while resonant processes are shown to produce the Planckian behavior.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.
Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ( T ) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large- N limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in- T resistivity with a universal “Planckian” transport scattering rate Γ tr ∼ k B T / ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.
We numerically study a model of interacting spin-1/21/21/2 electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by TTT-linear Planckian behavior, $\ensuremath{\omega}/T$ scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The $\ensuremath{\omega}/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a ``skewed'' non-Fermi liquid.
Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.