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:2310.20659 · Physical Review Research

Strange metal to insulator transitions in the lowest Landau level

Ben Currie, Evgeny Kozik

Published May 24, 2024• 1 citation
arXivHTMLPDF

Abstract

We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully filled Landau level. This critical point, as well as that of the SYK model—whose critical exponents we determine more precisely—are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings 0.2≲ν≲0.8 , while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially filled lowest Landau level at intermediate temperatures. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023210

Related papers

Non-Fermi liquid of extended range at zero temperature without quantum criticality

Tae-Ho Park, Han-Yong Choi

Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.

Scientific Reports•Apr 1, 2026•0 citations

Strange Metal Solution in the Diagrammatic Theory for the $2d$ Hubbard Model

Aaram J. Kim, Philipp Werner, Evgeny Kozik

We show that the numerically exact bold-line diagrammatic theory for the $2d$ Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the strong-interaction limit. The solution for the doped system features the expected phenomenology with the NFL near half-filling at strong couplings and in a wide temperature range enclosed by the atomic state at high temperatures and a Fermi liquid at low temperatures. We demonstrate, however, that this behavior in the weakly doped regime is due to the unphysical branch of the Luttinger-Ward functional. On the other hand, our analysis shows that the NFL physics is realized at larger doping.

arXiv:2012.06159•Dec 11, 2020•8 citations

Non-Fermi liquid over extended range at zero temperature without quantum criticality

Tae-Ho Park, Han-Yong Choi

A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.

arXiv:2408.14858•Aug 27, 2024•0 citations

Phase diagram of the spin- 12 Yukawa–Sachdev-Ye-Kitaev model: Non-Fermi liquid, insulator, and superconductor

Wei Wang, Andrew Davis, Gaopei Pan +2 more

We analyze the phase diagram of the spin-$\frac{1}{2}$ Yukawa--Sachdev-Ye-Kitaev model, which describes complex spin-$\frac{1}{2}$ fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. A recent work [Wang and Chubukov, Phys. Rev. Res. 2, 033084 (2020).] showed that, upon varying the filling or chemical potential, a first-order quantum phase transition exists between a non-Fermi-liquid (NFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be NFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on the parameters, the first-order quantum phase transition extends to finite temperatures and terminates at a thermal critical point, beyond which the NFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide a model realization of the transition of NFLs towards superconductivity and insulating states and therefore offer a controlled platform for future investigations of the generic phase diagram that hosts a NFL, insulator, and superconductor and their phase transitions.

arXiv:2102.10755•Physical review. B./Physical review. B•May 5, 2021•34 citations

Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing

Evyatar Tulipman, Noga Bashan, Jörg Schmalian +1 more

Strange metal behavior is traditionally associated with an underlying putative quantum critical point at zero temperature. However, in many correlated metals, e.g., high-${T}_{c}$ cuprate superconductors, strange metallicity persists at low temperatures over an extended range of microscopic parameters, suggesting the existence of an underlying quantum critical phase, whose possible physical origins remain poorly understood. Systematic investigations of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL) phase are therefore crucial to better understand this puzzling behavior. In a previous study [Bashan et al., Phys. Rev. Lett. 132, 236501 (2024)], we considered a solvable large-$N$ model consisting of itinerant electrons coupled to local two-level systems (TLSs) via spatially random interactions, inspired by the possibility of emergent metallic glassiness due to frustrated competing orders, and found that the system hosts an NFL phase with tunable exponents at intermediate couplings. In this paper, we expand our investigation to the following: (i) We study the extent to which this NFL phase is generic by considering various deformations of our theory, including coupling of electrons to multiple operators of the TLSs and arbitrarily directed TLS fields. We find that the physical picture obtained in Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)] qualitatively persist in a wide region of parameter space, showcasing the robustness of the NFL phase. (ii) We analyze the superconducting instability caused by the coupling of TLSs to electrons, and find a rich structure, including quantum critical pairing associated with the NFL phase and conventional BCS-like pairing in the weak and strong coupling limits. (iii) We elaborate on the analysis of Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)], including single-particle, transport, and thermodynamic properties.

arXiv:2404.06532•Physical review. B./Physical review. B•Oct 9, 2024•15 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
We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully filled Landau level. This critical point, as well as that of the SYK model—whose critical exponents we determine more precisely—are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings 0.2≲ν≲0.8 , while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially filled lowest Landau level at intermediate temperatures. Published by the American Physical Society 2024
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.
Strange Metal Solution in the Diagrammatic Theory for the 2d2d2d Hubbard Model
We show that the numerically exact bold-line diagrammatic theory for the 2d2d2d Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the strong-interaction limit. The solution for the doped system features the expected phenomenology with the NFL near half-filling at strong couplings and in a wide temperature range enclosed by the atomic state at high temperatures and a Fermi liquid at low temperatures. We demonstrate, however, that this behavior in the weakly doped regime is due to the unphysical branch of the Luttinger-Ward functional. On the other hand, our analysis shows that the NFL physics is realized at larger doping.
A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.
We analyze the phase diagram of the spin-12\frac{1}{2}21​ Yukawa--Sachdev-Ye-Kitaev model, which describes complex spin-12\frac{1}{2}21​ fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. A recent work [Wang and Chubukov, Phys. Rev. Res. 2, 033084 (2020).] showed that, upon varying the filling or chemical potential, a first-order quantum phase transition exists between a non-Fermi-liquid (NFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be NFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on the parameters, the first-order quantum phase transition extends to finite temperatures and terminates at a thermal critical point, beyond which the NFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide a model realization of the transition of NFLs towards superconductivity and insulating states and therefore offer a controlled platform for future investigations of the generic phase diagram that hosts a NFL, insulator, and superconductor and their phase transitions.
Strange metal behavior is traditionally associated with an underlying putative quantum critical point at zero temperature. However, in many correlated metals, e.g., high-Tc{T}_{c}Tc​ cuprate superconductors, strange metallicity persists at low temperatures over an extended range of microscopic parameters, suggesting the existence of an underlying quantum critical phase, whose possible physical origins remain poorly understood. Systematic investigations of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL) phase are therefore crucial to better understand this puzzling behavior. In a previous study [Bashan et al., Phys. Rev. Lett. 132, 236501 (2024)], we considered a solvable large-NNN model consisting of itinerant electrons coupled to local two-level systems (TLSs) via spatially random interactions, inspired by the possibility of emergent metallic glassiness due to frustrated competing orders, and found that the system hosts an NFL phase with tunable exponents at intermediate couplings. In this paper, we expand our investigation to the following: (i) We study the extent to which this NFL phase is generic by considering various deformations of our theory, including coupling of electrons to multiple operators of the TLSs and arbitrarily directed TLS fields. We find that the physical picture obtained in Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)] qualitatively persist in a wide region of parameter space, showcasing the robustness of the NFL phase. (ii) We analyze the superconducting instability caused by the coupling of TLSs to electrons, and find a rich structure, including quantum critical pairing associated with the NFL phase and conventional BCS-like pairing in the weak and strong coupling limits. (iii) We elaborate on the analysis of Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)], including single-particle, transport, and thermodynamic properties.
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.