Kevin D. Stubbs
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Kevin D. Stubbs has a total of 43 co-authors. Here are the top co-authors by number of shared publications:
- Lin Lin
University of California
9 shared publications - Jianfeng Lu
Duke University
7 shared publications - Alexander B. Watson
School of Mathematics, University of Minnesota, Minneapolis, MN 55455 USA
3 shared publications - Raehyun Kim
University of California, Berkeley
3 shared publications - Simon Becker
Institute for Mathematical Research, ETH Zurich, Zurich, Switzerland
3 shared publications - Allan H. MacDonald
Department of Physics, University of Texas at Austin, Austin, USA
2 shared publications
Latest Publications
- 28 September 2026
- Published by American Physical Society (APS) in Physical Review B
- Vol. 114 (18) , 185131
Ab initio quantum embedding description of magic-angle twisted bilayer graphene at even-integer fillings
The correlated phase diagram of magic-angle twisted bilayer graphene (MATBG) is very sensitive to both material parameters and modeling choices. To limit the impact of these factors, here, the authors propose an embedding workflow for modeling MATBG and other moir\'e materials that incorporates automatic gauge fixing and is consistent with $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ density functional theory. Using this workflow, the authors find that in MATBG, the Hartree-Fock ground state at $\ensuremath{\nu}=\ensuremath{-}2$ is a fragile semimetal with intervalley coherence.- 28 September 2026
- Published by American Physical Society (APS) in Physical Review B
- Vol. 114 (18) , 185131
Ab initio quantum embedding description of magic-angle twisted bilayer graphene at even-integer fillings
The correlated phase diagram of magic-angle twisted bilayer graphene (MATBG) is very sensitive to both material parameters and modeling choices. To limit the impact of these factors, here, the authors propose an embedding workflow for modeling MATBG and other moir\'e materials that incorporates automatic gauge fixing and is consistent with $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ density functional theory. Using this workflow, the authors find that in MATBG, the Hartree-Fock ground state at $\ensuremath{\nu}=\ensuremath{-}2$ is a fragile semimetal with intervalley coherence.- Open Access
- 27 September 2026
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 407 (11) , 236
Many-Body Ground State Manifold of Flat Band Interacting Hamiltonian for Magic Angle Twisted Bilayer Graphene
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic Slater determinants as exact ground states of the corresponding flat band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes the behavior of electrons that interact with each other in a high-dimensional space, and is constructed from the band structure of the non-interacting Bistritzer–MacDonald model at the chiral limit. A key property of the FBI Hamiltonian for MATBG is that it is frustration-free and can be written as a sum of non-commuting terms. In this work, we provide a complete characterization of the ground state manifold of the FBI Hamiltonian, proving that it is precisely the linear span of such ferromagnetic Slater determinants.
- 27 September 2026
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 407 (11) , 236
Open AccessMany-Body Ground State Manifold of Flat Band Interacting Hamiltonian for Magic Angle Twisted Bilayer Graphene
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic Slater determinants as exact ground states of the corresponding flat band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes the behavior of electrons that interact with each other in a high-dimensional space, and is constructed from the band structure of the non-interacting Bistritzer–MacDonald model at the chiral limit. A key property of the FBI Hamiltonian for MATBG is that it is frustration-free and can be written as a sum of non-commuting terms. In this work, we provide a complete characterization of the ground state manifold of the FBI Hamiltonian, proving that it is precisely the linear span of such ferromagnetic Slater determinants.
- Open Access
- 20 September 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (5) , 90
Algebraic Localization Implies Exponential Localization in Non-periodic Insulators
Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized Wannier functions exist if and only if there exists an orthonormal basis for the Fermi projection with finite second moment (that is all basis elements satisfy $$\int \vert \varvec{x}\vert ^2 \vert w(\varvec{x})\vert ^2 \,\text {d}{\varvec{x}} < \infty $$ ). In this work, we establish a similar result for non-periodic insulators in two spatial dimensions. In particular, we prove that if there exists an orthonormal basis for the Fermi projection which satisfies $$\int \vert \varvec{x}\vert ^{5 + \varepsilon } \vert w(\varvec{x})\vert ^2 \,\text {d}{\varvec{x}} < \infty $$ for some $$\varepsilon > 0$$ , then there also exists an orthonormal basis for the Fermi projection which decays exponentially fast in space. This result lends support to the Localization Dichotomy Conjecture for non-periodic systems recently proposed by Marcelli, Monaco, Moscolari, and Panati in [1, 2].- 20 September 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (5) , 90
Open AccessAlgebraic Localization Implies Exponential Localization in Non-periodic Insulators
Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized Wannier functions exist if and only if there exists an orthonormal basis for the Fermi projection with finite second moment (that is all basis elements satisfy $$\int \vert \varvec{x}\vert ^2 \vert w(\varvec{x})\vert ^2 \,\text {d}{\varvec{x}} < \infty $$ ). In this work, we establish a similar result for non-periodic insulators in two spatial dimensions. In particular, we prove that if there exists an orthonormal basis for the Fermi projection which satisfies $$\int \vert \varvec{x}\vert ^{5 + \varepsilon } \vert w(\varvec{x})\vert ^2 \,\text {d}{\varvec{x}} < \infty $$ for some $$\varepsilon > 0$$ , then there also exists an orthonormal basis for the Fermi projection which decays exponentially fast in space. This result lends support to the Localization Dichotomy Conjecture for non-periodic systems recently proposed by Marcelli, Monaco, Moscolari, and Panati in [1, 2]. - 28 August 2025
- Published by Society for Industrial & Applied Mathematics (SIAM) in Multiscale Modeling & Simulation
- Vol. 23 (3) , 1333-1357
On the Hartree–Fock Ground State Manifold in Magic Angle Twisted Graphene Systems
Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG have shown that Hartree–Fock ground states (with a positive single-particle excitation gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree–Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree–Fock ground state manifold, which is generated by a [Formula: see text] hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree–Fock ground state manifold, which may be of independent interest.
- 28 August 2025
- Published by Society for Industrial & Applied Mathematics (SIAM) in Multiscale Modeling & Simulation
- Vol. 23 (3) , 1333-1357
On the Hartree–Fock Ground State Manifold in Magic Angle Twisted Graphene Systems
Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG have shown that Hartree–Fock ground states (with a positive single-particle excitation gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree–Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree–Fock ground state manifold, which is generated by a [Formula: see text] hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree–Fock ground state manifold, which may be of independent interest.
- Open Access
- 2 July 2025
- Published by IOP Publishing in Electronic Structure
- Vol. 7 (3)
Interacting Twisted Bilayer Graphene with Systematic Modeling of Structural Relaxation
Twisted bilayer graphene (TBG) has drawn significant interest due to recent experiments which show that TBG can exhibit strongly correlated behavior such as the superconducting and correlated insulator phases. Much of the theoretical work on TBG has been based on analysis of the Bistritzer-MacDonald model which includes a phenomenological parameter to account for lattice relaxation. In this work, we use a newly developed continuum model which systematically accounts for the effects of structural relaxation. In particular, we model structural relaxation by coupling linear elasticity to a stacking energy that penalizes disregistry. We compare the impact of the two relaxation models on the corresponding many-body model by defining an interacting model projected to the flat bands. We perform tests at charge neutrality at both the Hartree-Fock and Coupled Cluster Singles and Doubles (CCSD) level of theory and find the systematic relaxation model gives quantitative differences from the simplified relaxation model.
- 2 July 2025
- Published by IOP Publishing in Electronic Structure
- Vol. 7 (3)
Open AccessInteracting Twisted Bilayer Graphene with Systematic Modeling of Structural Relaxation
Twisted bilayer graphene (TBG) has drawn significant interest due to recent experiments which show that TBG can exhibit strongly correlated behavior such as the superconducting and correlated insulator phases. Much of the theoretical work on TBG has been based on analysis of the Bistritzer-MacDonald model which includes a phenomenological parameter to account for lattice relaxation. In this work, we use a newly developed continuum model which systematically accounts for the effects of structural relaxation. In particular, we model structural relaxation by coupling linear elasticity to a stacking energy that penalizes disregistry. We compare the impact of the two relaxation models on the corresponding many-body model by defining an interacting model projected to the flat bands. We perform tests at charge neutrality at both the Hartree-Fock and Coupled Cluster Singles and Doubles (CCSD) level of theory and find the systematic relaxation model gives quantitative differences from the simplified relaxation model.
- Open Access
- 30 May 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (6) , 1-51
Exact Ground State of Interacting Electrons in Magic Angle Graphene
One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi- $${\theta }$$ and Weierstrass- $${\wp }$$ functions.- 30 May 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (6) , 1-51
Open AccessExact Ground State of Interacting Electrons in Magic Angle Graphene
One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi- $${\theta }$$ and Weierstrass- $${\wp }$$ functions. - Open Access
The Many-Body Ground State Manifold of Flat Band Interacting Hamiltonian for Magic Angle Twisted Bilayer Graphene
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic Slater determinants as exact ground states of the corresponding flat band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes the behavior of electrons that interact with each other in a high-dimensional space, and is constructed from the band structure of the non-interacting Bistritzer--MacDonald model at the chiral limit. A key property of the FBI Hamiltonian for MATBG is that it is frustration free and can be written as a sum of non-commuting terms. In this work, we provide a complete characterization of the ground state manifold of the FBI Hamiltonian, proving that it is precisely the linear span of such ferromagnetic Slater determinants.
Open AccessThe Many-Body Ground State Manifold of Flat Band Interacting Hamiltonian for Magic Angle Twisted Bilayer Graphene
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic Slater determinants as exact ground states of the corresponding flat band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes the behavior of electrons that interact with each other in a high-dimensional space, and is constructed from the band structure of the non-interacting Bistritzer--MacDonald model at the chiral limit. A key property of the FBI Hamiltonian for MATBG is that it is frustration free and can be written as a sum of non-commuting terms. In this work, we provide a complete characterization of the ground state manifold of the FBI Hamiltonian, proving that it is precisely the linear span of such ferromagnetic Slater determinants.
- Open Access
- 20 December 2024
- Published by American Physical Society (APS) in Physical Review Research
- Vol. 6 (4)
Erasure conversion in Majorana qubits via local quasiparticle detection
Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by the underlying topological properties, which undermines the usefulness of this proposed platform. This work tackles the errors originating from intrinsically excited quasiparticles by developing an erasure conversion scheme based on local quasiparticle detection. To model such measurements, we begin by constructing the quasiparticle position operator for the Kitaev chain. A measurement probe coupling to this operator is shown to allow projective measurements in the Wannier quasiparticle basis. Detection of quasiparticles in a region of width d adjacent to each Majorana zero-energy mode allows implementation of an error-detecting Majorana stabilizer code C d based on microscopic fermionic (nontopological) physical degrees of freedom. The implementation of C d converts a large fraction of Pauli errors to erasure errors, thus achieving “erasure conversion” in Majorana qubits. We show that the fraction of Pauli errors escaping conversion to erasure errors is exponentially small in d , a result tied to the exponential localization of Wannier functions which we prove rigorously. The suppression in Pauli error rate comes at the cost of the erasure rate increasing sublinearly with d , but this can be readily compensated for by a suitable outer code, with the net effect being a higher threshold rate of quasiparticle poisoning. The framework developed here serves as a basis for understanding how realistic measurements, such as conductance measurements, could be utilized for achieving fault tolerance in these systems. Published by the American Physical Society 2024
- 20 December 2024
- Published by American Physical Society (APS) in Physical Review Research
- Vol. 6 (4)
Open AccessErasure conversion in Majorana qubits via local quasiparticle detection
Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by the underlying topological properties, which undermines the usefulness of this proposed platform. This work tackles the errors originating from intrinsically excited quasiparticles by developing an erasure conversion scheme based on local quasiparticle detection. To model such measurements, we begin by constructing the quasiparticle position operator for the Kitaev chain. A measurement probe coupling to this operator is shown to allow projective measurements in the Wannier quasiparticle basis. Detection of quasiparticles in a region of width d adjacent to each Majorana zero-energy mode allows implementation of an error-detecting Majorana stabilizer code C d based on microscopic fermionic (nontopological) physical degrees of freedom. The implementation of C d converts a large fraction of Pauli errors to erasure errors, thus achieving “erasure conversion” in Majorana qubits. We show that the fraction of Pauli errors escaping conversion to erasure errors is exponentially small in d , a result tied to the exponential localization of Wannier functions which we prove rigorously. The suppression in Pauli error rate comes at the cost of the erasure rate increasing sublinearly with d , but this can be readily compensated for by a suitable outer code, with the net effect being a higher threshold rate of quasiparticle poisoning. The framework developed here serves as a basis for understanding how realistic measurements, such as conductance measurements, could be utilized for achieving fault tolerance in these systems. Published by the American Physical Society 2024
- 12 June 2024
- Published by Springer Nature in Annales Henri Poincare
- Vol. 25 (8) , 3911-3926
Algebraic Localization of Wannier Functions Implies Chern Triviality in Non-periodic Insulators
- 12 June 2024
- Published by Springer Nature in Annales Henri Poincare
- Vol. 25 (8) , 3911-3926
Algebraic Localization of Wannier Functions Implies Chern Triviality in Non-periodic Insulators
- Open Access
On the Hartree-Fock Ground State Manifold in Magic Angle Twisted Graphene Systems
Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG has shown that Hartree-Fock ground states (with a positive charge gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree-Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree-Fock ground state manifold, which is generated by a ${\rm U}(4) \times {\rm U}(4)$ hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree-Fock ground state manifold, which may be of independent interest.Open AccessOn the Hartree-Fock Ground State Manifold in Magic Angle Twisted Graphene Systems
Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG has shown that Hartree-Fock ground states (with a positive charge gap) can be exact many-body ground states of an idealized flat band interacting (FBI) Hamiltonian. We prove that in the absence of spin and valley degrees of freedom, the only Hartree-Fock ground states of the FBI Hamiltonian for MATBG are two ferromagnetic Slater determinants. Incorporating spin and valley degrees of freedom, we provide a complete characterization of the Hartree-Fock ground state manifold, which is generated by a ${\rm U}(4) \times {\rm U}(4)$ hidden symmetry group acting on five elements. We also introduce new tools for ruling out translation symmetry breaking in the Hartree-Fock ground state manifold, which may be of independent interest.