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:2410.13858

Monte Carlo Study of Critical Fermi Surface with Spatially Disordered Interactions

Hong, Tu, Xiao Yan Xu

Published Oct 17, 2024• 1 citation
arXivHTMLPDF

Abstract

Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite $N$, beyond the large-$N$ used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the $ω\ln ω$ type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.

DOI
10.48550/arxiv.2410.13858

Related papers

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

Resilient strange metal at an unconventional quantum critical point in $d=2$

Jérôme Leblanc, A.–M. S. Tremblay

Properties of the two-dimensional Hubbard model with nearest-neighbor hopping are under scrutiny in cold-atom experiments and diagrammatic quantum Monte Carlo. Given the controlled nature of these approaches, it is timely to make predictions about strange-metal behavior and its relation to quantum-critical properties. Even for interaction strengths below the Mott transition, several peculiarities occur at the quantum critical point separating Fermi liquid and incommensurate spin-density wave order. Here, we predict, using the non-perturbative improved two-particle self-consistent approach, that for correlation lengths ranging from about one to one hundred lattice spacings, Kohn anomalies on the underlying Fermi surface lead to unconventional critical exponents. The temperature dependence of the single-particle self-energy acquires strong momentum dependence along the Fermi surface with no clear evidence of Landau quasiparticles. Nevertheless, we observe strange-metal behavior, namely, resistivity that scales linearly with temperature as $T\rightarrow{0}$. Our work shows that a linear temperature dependence of resistivity arises without a linear-in-temperature self-energy along the Fermi surface, as is often assumed.

arXiv:2608.05988•Aug 6, 2026•0 citations

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

Simulating and machine learning quantum criticality in a nearly antiferromagnetic metal

Carsten Bauer

In the last few decades, quantum criticality in itinerant electron systems has become a central focus of condensed matter physics. On the one hand, it represents a candidate mechanism for high-temperature superconductivity. On the other hand, it can lead to a breakdown of Fermi liquid theory. The formation of a comprehensive understanding of metallic quantum criticality has, however, been significantly hampered by the fact that in many-fermion systems, fluctuations of a critical order parameter can couple to extensive gapless modes on a finite Fermi surface. This interplay, while giving rise to intriguing physical phenomena, leads to strong electronic correlations, which are notoriously difficult to handle by analytic methods. In this thesis, we investigate metallic quantum criticality by means of large-scale quantum Monte Carlo simulations and contribute unbiased, rigorous results to the discussion. Focusing on antiferromagnetic spin-density wave ordering, we present the numerically exact phase diagram of a spin-fermion model whose solution has so far been out of reach. In particular, we highlight the emergence of high-temperature d-wave superconductivity and rigorously establish the quantum critical properties of the antiferromagnetic quantum critical point. Combining the Monte Carlo method with a quantum loop topography approach, we demonstrate that important features of quantum critical metals can be autonomously identified by machine learning of current-current correlations. This allows us to analyze the electronic transport characteristics of two quantum critical metals, including the spin-fermion model, over a large parameter range and leads to the identification of extended non-Fermi liquid regimes in their respective phase diagrams.

•Feb 1, 2021•2 citations

Monte Carlo Studies of Quantum Critical Metals

Erez Berg, Samuel Lederer, Yoni Schattner +1 more

Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.

arXiv:1804.01988•Annual Review of Condensed Matter Physics•Nov 16, 2018•104 citations

Doping a Mott insulator in an Ising-Kondo lattice: Strange metal and Mott criticality

Wei-Wei Yang, Yin-Xia Li, Yin Zhong +1 more

Metallic quantum states coined strange metal (SM), with robust linear-$T$ resistivity, have been widely observed in many quantum materials under strong electron correlations, ranging from high-${T}_{c}$ cuprate superconductors and organic superconductors to twisted multilayer graphene and ${\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}$ superlattices. Despite decades of intensive studies, the mystery of SM still defies any sensible theoretical explanation and has been a key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model called an Ising-Kondo lattice, which includes static spin fluctuation. With Monte Carlo simulation, the Ising-Kondo lattice unambiguously exhibits SM phenomena accompanied with quantum critical scaling in observables, e.g., resistivity, susceptibility, and specific heat. A closer look at SM reveals the breakdown of Landau's Fermi liquid theory without any symmetry breaking, i.e., the violation of Luttinger theorem. Our paper reveals that the long-overlooked static fluctuations in literature may play an essential role in non-Fermi liquid behaviors in correlated electron systems.

arXiv:2101.10611•Physical review. B./Physical review. B•Oct 27, 2021•8 citations
Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite NNN, beyond the large-NNN used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the ωln⁡ωω\ln ωωlnω type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.
“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.
Resilient strange metal at an unconventional quantum critical point in d=2d=2d=2
Properties of the two-dimensional Hubbard model with nearest-neighbor hopping are under scrutiny in cold-atom experiments and diagrammatic quantum Monte Carlo. Given the controlled nature of these approaches, it is timely to make predictions about strange-metal behavior and its relation to quantum-critical properties. Even for interaction strengths below the Mott transition, several peculiarities occur at the quantum critical point separating Fermi liquid and incommensurate spin-density wave order. Here, we predict, using the non-perturbative improved two-particle self-consistent approach, that for correlation lengths ranging from about one to one hundred lattice spacings, Kohn anomalies on the underlying Fermi surface lead to unconventional critical exponents. The temperature dependence of the single-particle self-energy acquires strong momentum dependence along the Fermi surface with no clear evidence of Landau quasiparticles. Nevertheless, we observe strange-metal behavior, namely, resistivity that scales linearly with temperature as T→0T\rightarrow{0}T→0. Our work shows that a linear temperature dependence of resistivity arises without a linear-in-temperature self-energy along the Fermi surface, as is often assumed.
"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.
In the last few decades, quantum criticality in itinerant electron systems has become a central focus of condensed matter physics. On the one hand, it represents a candidate mechanism for high-temperature superconductivity. On the other hand, it can lead to a breakdown of Fermi liquid theory. The formation of a comprehensive understanding of metallic quantum criticality has, however, been significantly hampered by the fact that in many-fermion systems, fluctuations of a critical order parameter can couple to extensive gapless modes on a finite Fermi surface. This interplay, while giving rise to intriguing physical phenomena, leads to strong electronic correlations, which are notoriously difficult to handle by analytic methods. In this thesis, we investigate metallic quantum criticality by means of large-scale quantum Monte Carlo simulations and contribute unbiased, rigorous results to the discussion. Focusing on antiferromagnetic spin-density wave ordering, we present the numerically exact phase diagram of a spin-fermion model whose solution has so far been out of reach. In particular, we highlight the emergence of high-temperature d-wave superconductivity and rigorously establish the quantum critical properties of the antiferromagnetic quantum critical point. Combining the Monte Carlo method with a quantum loop topography approach, we demonstrate that important features of quantum critical metals can be autonomously identified by machine learning of current-current correlations. This allows us to analyze the electronic transport characteristics of two quantum critical metals, including the spin-fermion model, over a large parameter range and leads to the identification of extended non-Fermi liquid regimes in their respective phase diagrams.
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
Metallic quantum states coined strange metal (SM), with robust linear-TTT resistivity, have been widely observed in many quantum materials under strong electron correlations, ranging from high-Tc{T}_{c}Tc​ cuprate superconductors and organic superconductors to twisted multilayer graphene and MoTe2/WSe2{\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}MoTe2​/WSe2​ superlattices. Despite decades of intensive studies, the mystery of SM still defies any sensible theoretical explanation and has been a key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model called an Ising-Kondo lattice, which includes static spin fluctuation. With Monte Carlo simulation, the Ising-Kondo lattice unambiguously exhibits SM phenomena accompanied with quantum critical scaling in observables, e.g., resistivity, susceptibility, and specific heat. A closer look at SM reveals the breakdown of Landau's Fermi liquid theory without any symmetry breaking, i.e., the violation of Luttinger theorem. Our paper reveals that the long-overlooked static fluctuations in literature may play an essential role in non-Fermi liquid behaviors in correlated electron systems.