Exotic quantum criticality in Dirac systems: Metallic and deconfined

Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)

\times

U(1) symmetry. Using large-scale auxiliary- field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.

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Metallic and Deconfined Quantum Criticality in Dirac Systems

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Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×U(1) symmetry. Using large-scale auxiliary-field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition toward an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data are consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×U(1) symmetry. Using large-scale auxiliary-field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition toward an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data are consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.

arXiv:2108.06346Physical Review LettersFeb 23, 202232 citations

Critical properties of metallic and deconfined quantum phase transitions in Dirac systems

Zi Hong Liu, Matthias Vojta C, Fakher F. Assaad +1 more

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Exotic quantum phase transitions of strongly interacting topological insulators

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Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin ${S}^{z}$ conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the ${\mathbb{Z}}_{16}$ classification of the topological superconductor $^{3}\mathrm{He}\text{\ensuremath{-}}B$ phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic $O(4)$ nonlinear sigma model field theory with a $\ensuremath{\Theta}$ term.Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin ${S}^{z}$ conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the ${\mathbb{Z}}_{16}$ classification of the topological superconductor $^{3}\mathrm{He}\text{\ensuremath{-}}B$ phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic $O(4)$ nonlinear sigma model field theory with a $\ensuremath{\Theta}$ term.

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Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice

Yuichi Otsuka, Kazuhiro Seki, Sandro Sorella +1 more

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arXiv:1803.02001Physical review. B./Physical review. BJul 18, 201831 citations

Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)

\times

(2+1)

-dimensional Gross-Neveu-SO(3) field theory. By performing simulations with an improved symmetric Trotter decomposition, we further substantiate this claim by computing the critical exponents $1/\ensuremath{\nu}$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}$, which turn out to be consistent with the field-theoretical expectation within numerical and analytical uncertainties. The second transition between the two long-range-ordered phases has previously been proposed as a possible instance of a metallic deconfined quantum critical point. We further develop this scenario by analyzing the spectral functions in the single-particle, particle-hole, and particle-particle channels. Our results indicate gapless excitations with a unique velocity, supporting the emergence of Lorentz symmetry at criticality. We also compute the finite-temperature phase boundaries of the ordered states above the fully gapped state at large interaction. The phase boundary vanishes smoothly in the vicinity of the putative metallic deconfined quantum critical point, in agreement with the expectation for a continuous or weakly first-order transition.

{S}^{z}

conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the

{\mathbb{Z}}_{16}

classification of the topological superconductor $^{3}\mathrm{He}\text{\ensuremath{-}}B$ phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic

O(4)

nonlinear sigma model field theory with a $\ensuremath{\Theta}$ term.

U(1)

symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the

s

-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent

U(1)

symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].