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:1705.09192 · Physical review. B./Physical review. B

Dynamical generation of topological masses in Dirac fermions

Yuan-Yao He, Xiao Yan Xu, Kai Sun, Fakher F. Assaad, Zi Yang Meng, Zhong-Yi Lu

Published Feb 22, 2018• 38 citations
arXivHTMLPDF

Abstract

Using large-scale quantum Monte Carlo simulations, the authors unbiasedly demonstrate the existence of a topological Mott insulator -- an interaction-driven topological insulator emerging from a strongly correlated Dirac semimetal. The model designed here consists of Dirac fermions and fluctuating Ising fields mediating interactions between fermions. By tuning the fluctuation strength of the Ising fields, the authors show the existence of a topological quantum phase transition between the topological Mott insulator phase and the Dirac-semimetal phase. Furthermore, the quantum critical point was found to be in the (2+1)D $N$=8 Chiral Ising universality class.

DOI
10.1103/physrevb.97.081110

Related papers

Topological phase transitions with SO(4) symmetry in (2+1)D interacting Dirac fermions

Xiao Yan Xu, K. S. D. Beach, Kai Sun +2 more

Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground-state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.

arXiv:1602.07150•Physical review. B./Physical review. B•Feb 7, 2017•21 citations

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

Yuan-Yao He, Han-Qing Wu, Yi‐Zhuang You +3 more

We study a lattice model of interacting Dirac fermions in $(2+1)$ dimensions space-time with an SU(4) symmetry. While increasing the interaction strength, this model undergoes a continuous quantum phase transition from a weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progress in the lattice QCD community.

arXiv:1603.08376•Physical review. B./Physical review. B•Dec 20, 2016•32 citations

Localization of Interacting Dirac Fermions

Tianxing Ma, Lufeng Zhang, Chia‐Chen Chang +2 more

Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.

arXiv:1611.00047•Physical Review Letters•Mar 12, 2018•46 citations

Critical behavior of Dirac fermions from perturbative renormalization

Bernhard Ihrig, Luminita N. Mihaila, Michael M. Scherer

Near the critical point of a phase transition, physical observables are characterized by a set of pure numbers -- the critical exponents -- which are identical for a whole class of transitions defining a ``universality class''. Novel Dirac materials exhibit quantum critical points, which are not captured by conventional universality classes and their description defines new challenges for theory. The authors present here a comprehensive renormalization group study and give quantitative predictions for universality classes of Dirac fermions, as relevant to semimetal-insulator transitions in graphene and emergent supersymmetry in topological insulators. The authors also compare to independent conformal bootstrap results and quantum Monte Carlo estimates.

arXiv:1806.04977•Physical review. B./Physical review. B•Sep 5, 2018•76 citations

Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition

Yuan Da Liao, Xiao Yan Xu, Zi Yang Meng +1 more

Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the $\mathrm{SU}(N)$ Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.

arXiv:2207.13349•Physical review. B./Physical review. B•Oct 31, 2022•15 citations

Quantum fluctuations and criticality of interacting Dirac fermions.

Elliot Christou

This Thesis explores the formation of novel phases in Dirac systems that are driven by strong many-body interactions and collective quantum fluctuations. The central focus is the half-filled honeycomb lattice, which is the prototypical Dirac semimetal with low-energy excitations described by Dirac fermions. Of particular interest are exotic phases of matter that are not favoured at mean-field but are stabilised by fluctuations. Self-consistent path integral techniques are used to demonstrate that extended repulsive interactions favour charge order that breaks translational and other lattice symmetries. This charge order outcompetes interaction induced topological insulating phases, which are dominant at the mean-field level. The interacting quantum critical point was found to be near the critical point of a topological Lifshitz transition. Interacting Dirac fermions exhibit perhaps the simplest example of fermionic quantum criticality. Gross-Neveu-Yukawa field theories describe the universality class of semimetal-insulator transitions, which are driven by on-site and nearest neighbour repulsive interactions on the honeycomb lattice. The Dirac fermions couple to the dynamical order parameter fields and play a crucial role in determining the universal behaviour. Naturally, this variety of criticality is outside of the Ginzburg-Landau-Wilson paradigm. This idea is extended to include the translational symmetry breaking charge order. Here it is found that the breaking of crystal symmetries corresponds to Lorentz violating effective field theories. The criticality is analysed with the renormalisation group. The low energy excitations at the topological transition are gapless semi-Dirac fermionic quasiparticles that disperse linearly in one direction and quadratically in the other. The instabilities induced by generic short-range repulsions are investigated. The criticality of this anisotropic system is analysed with the renormalisation group in two spatial dimensions, and it is found to exhibit anisotropic order parameter correlations.

•Oct 28, 2019•0 citations
Using large-scale quantum Monte Carlo simulations, the authors unbiasedly demonstrate the existence of a topological Mott insulator -- an interaction-driven topological insulator emerging from a strongly correlated Dirac semimetal. The model designed here consists of Dirac fermions and fluctuating Ising fields mediating interactions between fermions. By tuning the fluctuation strength of the Ising fields, the authors show the existence of a topological quantum phase transition between the topological Mott insulator phase and the Dirac-semimetal phase. Furthermore, the quantum critical point was found to be in the (2+1)D NNN=8 Chiral Ising universality class.
Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground-state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.
We study a lattice model of interacting Dirac fermions in (2+1)(2+1)(2+1) dimensions space-time with an SU(4) symmetry. While increasing the interaction strength, this model undergoes a continuous quantum phase transition from a weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progress in the lattice QCD community.
Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.
Near the critical point of a phase transition, physical observables are characterized by a set of pure numbers -- the critical exponents -- which are identical for a whole class of transitions defining a ``universality class''. Novel Dirac materials exhibit quantum critical points, which are not captured by conventional universality classes and their description defines new challenges for theory. The authors present here a comprehensive renormalization group study and give quantitative predictions for universality classes of Dirac fermions, as relevant to semimetal-insulator transitions in graphene and emergent supersymmetry in topological insulators. The authors also compare to independent conformal bootstrap results and quantum Monte Carlo estimates.
Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the SU(N)\mathrm{SU}(N)SU(N) Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.
This Thesis explores the formation of novel phases in Dirac systems that are driven by strong many-body interactions and collective quantum fluctuations. The central focus is the half-filled honeycomb lattice, which is the prototypical Dirac semimetal with low-energy excitations described by Dirac fermions. Of particular interest are exotic phases of matter that are not favoured at mean-field but are stabilised by fluctuations. Self-consistent path integral techniques are used to demonstrate that extended repulsive interactions favour charge order that breaks translational and other lattice symmetries. This charge order outcompetes interaction induced topological insulating phases, which are dominant at the mean-field level. The interacting quantum critical point was found to be near the critical point of a topological Lifshitz transition. Interacting Dirac fermions exhibit perhaps the simplest example of fermionic quantum criticality. Gross-Neveu-Yukawa field theories describe the universality class of semimetal-insulator transitions, which are driven by on-site and nearest neighbour repulsive interactions on the honeycomb lattice. The Dirac fermions couple to the dynamical order parameter fields and play a crucial role in determining the universal behaviour. Naturally, this variety of criticality is outside of the Ginzburg-Landau-Wilson paradigm. This idea is extended to include the translational symmetry breaking charge order. Here it is found that the breaking of crystal symmetries corresponds to Lorentz violating effective field theories. The criticality is analysed with the renormalisation group. The low energy excitations at the topological transition are gapless semi-Dirac fermionic quasiparticles that disperse linearly in one direction and quadratically in the other. The instabilities induced by generic short-range repulsions are investigated. The criticality of this anisotropic system is analysed with the renormalisation group in two spatial dimensions, and it is found to exhibit anisotropic order parameter correlations.