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:2605.20677 · Physical review. B./Physical review. B

Strain-tuned incommensurate Kekulé spiral order in twisted bilayer graphene: A quantum many-body study

Cheng Huang, Yves H. Kwan, Maksim Ulybyshev, Fakher F. Assaad, Laura Classen, Zi Yang Meng

Published Sep 29, 2026• 0 citations
arXivHTMLPDF

Abstract

The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factor $ν=\pm2$ and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED) and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly-correlated systems.

DOI
10.1103/f3zp-8s7c

Related papers

Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene

Johannes Stephan Hofmann, Eslam Khalaf, Ashvin Vishwanath +2 more

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

arXiv:2105.12112•Physical Review X•Mar 30, 2022•73 citations

Angle-tuned Gross-Neveu quantum criticality in twisted bilayer graphene

Cheng Huang, Nikolaos Parthenios, Maksim Ulybyshev +4 more

Abstract Twisted bilayber graphene (TBG) has revealed fascinating quantum many-body states, and unstrained chargeneutral TBG at 1.08° is understood, both experimentally and theoretically , as a correlated insulator due to the interplay of long-range Coulomb interactions and the quantum metrics of flat bands. However, the fate of the ground state as one continuously tunes the twisted angle is still largely unknown. Here, theoretically, by employing a newly developed momentum-space continuous-field quantum Monte Carlo method that can fully take into account the long-range Coulomb interactions and quantum metrics of flat bands with system sizes that were not possible before , we show that charge-neutral TBG realizes an angle-tuned quantum phase transition with Gross-Neveu criticality at Θc ~ 1.20(1)°, from the analyses of single-particle spectra, free energy and the order parameter of inter-valley coherence. This shows the exciting possibility that by tuning away from 1.08°, pristine TBG can mimic a fundamental phase transition of Dirac fermions.

arXiv:2412.11382•Nature Communications•Aug 4, 2025•15 citations

Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study

Zhi-Yu Xiao, Shiwei Zhang

Magic-angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings or smaller lattice sizes. We employ a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers intervalley-coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.

arXiv:2405.17808•Physical Review Research•Jan 27, 2025•3 citations

Trion Excitations in Twisted Bilayer Graphene: A Quantum Monte Carlo Study

Shibo Shan, Cheng Huang, Patrick Ledwith +1 more

Determining the nature of charge carriers is a fundamental goal in the study of strongly correlated electron systems. Here, we employ the continuous-field momentum-space quantum Monte Carlo method to reveal exotic "Dirac trion" excitations in the finite-temperature normal state of twisted bilayer graphene. While the ground state is a symmetry-breaking insulator with gapped ($\sim$ 20 meV) electron-like excitations, we show that a small temperature ($\sim$ 3 meV), well below the interaction scale, drives the system into a strongly fluctuating symmetric normal state. We demonstrate that this normal state hosts gapless excitations consisting of three-particle bound states, two electrons and one hole, that are exactly orthogonal to the higher-energy electrons at the zero-momentum gapless point. These Dirac trions have the remarkable property of being arbitrarily light despite being composed of heavy constituents, and their spectra can be easily tuned by varying the twist angle and interlayer hopping strength. Our unbiased quantum many-body computation sheds light on the Dirac trions in a projected correlated flat-band setting and opens the door for further investigation of many-body excitations in strongly correlated topological bands beyond Landau levels.

cond-mat.str-elCross-listedarXiv:2607.27745•Jul 31, 2026

Quantum Monte Carlo study of magnetic ordering and superconducting pairing symmetry in twisted bilayer graphene

Shi-Chao Fang, Guangkun Liu, Hai-Qing Lin +1 more

To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard $U$ is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the $d+id$ symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction $V$ results in a suppression of the $d+id$ superconductivity, but it can survive in the small $V$ regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.

Physical review. B./Physical review. B•Sep 16, 2019•16 citations

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

Xiao Yan Xu, K. T. Law, Patrick A. Lee

Motivated by recent experimental findings of correlating insulator and superconductor behavior in twisted bilayer graphene, the authors study a cluster charge interaction model on a honeycomb lattice. The cluster charge is defined on the dual lattice of honeycomb to mimic charge centers forming a triangular lattice found in experiments. Based on unbiased sign-problem-free quantum Monte Carlo simulations, the authors determine the phase diagram for this model. It features a fermionic quantum critical point with chiral XY universality and a Kekul\'e valence bond solid phase at intermediate interaction, which may be related to the correlating insulator phase found in experiments. This is an example of the rich phases found in a simple model without artificial design.

arXiv:1805.00478•Physical review. B./Physical review. B•Sep 13, 2018•158 citations
The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factor ν=±2ν=\pm2ν=±2 and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED) and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly-correlated systems.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.
Abstract Twisted bilayber graphene (TBG) has revealed fascinating quantum many-body states, and unstrained chargeneutral TBG at 1.08° is understood, both experimentally and theoretically , as a correlated insulator due to the interplay of long-range Coulomb interactions and the quantum metrics of flat bands. However, the fate of the ground state as one continuously tunes the twisted angle is still largely unknown. Here, theoretically, by employing a newly developed momentum-space continuous-field quantum Monte Carlo method that can fully take into account the long-range Coulomb interactions and quantum metrics of flat bands with system sizes that were not possible before , we show that charge-neutral TBG realizes an angle-tuned quantum phase transition with Gross-Neveu criticality at Θc ~ 1.20(1)°, from the analyses of single-particle spectra, free energy and the order parameter of inter-valley coherence. This shows the exciting possibility that by tuning away from 1.08°, pristine TBG can mimic a fundamental phase transition of Dirac fermions.
Magic-angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings or smaller lattice sizes. We employ a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers intervalley-coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.
Determining the nature of charge carriers is a fundamental goal in the study of strongly correlated electron systems. Here, we employ the continuous-field momentum-space quantum Monte Carlo method to reveal exotic "Dirac trion" excitations in the finite-temperature normal state of twisted bilayer graphene. While the ground state is a symmetry-breaking insulator with gapped (∼\sim∼ 20 meV) electron-like excitations, we show that a small temperature (∼\sim∼ 3 meV), well below the interaction scale, drives the system into a strongly fluctuating symmetric normal state. We demonstrate that this normal state hosts gapless excitations consisting of three-particle bound states, two electrons and one hole, that are exactly orthogonal to the higher-energy electrons at the zero-momentum gapless point. These Dirac trions have the remarkable property of being arbitrarily light despite being composed of heavy constituents, and their spectra can be easily tuned by varying the twist angle and interlayer hopping strength. Our unbiased quantum many-body computation sheds light on the Dirac trions in a projected correlated flat-band setting and opens the door for further investigation of many-body excitations in strongly correlated topological bands beyond Landau levels.
To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard UUU is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the d+idd+idd+id symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction VVV results in a suppression of the d+idd+idd+id superconductivity, but it can survive in the small VVV regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.
Motivated by recent experimental findings of correlating insulator and superconductor behavior in twisted bilayer graphene, the authors study a cluster charge interaction model on a honeycomb lattice. The cluster charge is defined on the dual lattice of honeycomb to mimic charge centers forming a triangular lattice found in experiments. Based on unbiased sign-problem-free quantum Monte Carlo simulations, the authors determine the phase diagram for this model. It features a fermionic quantum critical point with chiral XY universality and a Kekul\'e valence bond solid phase at intermediate interaction, which may be related to the correlating insulator phase found in experiments. This is an example of the rich phases found in a simple model without artificial design.