Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder-driven semimetal to metal quantum phase transition of three-dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field-theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low-energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent ( $z$ ) and correlation length exponent ($\ensuremath{\nu}$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field-theoretical analysis.Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder-driven semimetal to metal quantum phase transition of three-dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field-theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low-energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent ($z$) and correlation length exponent ($\ensuremath{\nu}$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field-theoretical analysis.

arXiv:1505.07938Physical review. B./Physical review. BFeb 1, 201661 citations

Spinless fermion model with quantum criticality

P. Schlottmann

Physica B Condensed MatterFeb 11, 20062 citations

Generic “unnecessary” quantum critical points with minimal degrees of freedom

Chao‐Ming Jian, Cenke Xu

We explore generic ``unnecessary'' quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions. In this work we seek for examples of generic unnecessary quantum critical points with minimal degrees of freedom. In particular, in three-dimensional space, we identify two examples of such generic unnecessary quantum critical points. The first example occurs in a $3d$ interacting topological insulator, and it is described by two $(3+1)d$ massless Dirac fermions in the infrared limit; the second example occurs in a $3d$ topological superconductor, and it is formally described by only one $(3+1)d$ massless Dirac fermion.We explore generic ``unnecessary'' quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions. In this work we seek for examples of generic unnecessary quantum critical points with minimal degrees of freedom. In particular, in three-dimensional space, we identify two examples of such generic unnecessary quantum critical points. The first example occurs in a $3d$ interacting topological insulator, and it is described by two $(3+1)d$ massless Dirac fermions in the infrared limit; the second example occurs in a $3d$ topological superconductor, and it is formally described by only one $(3+1)d$ massless Dirac fermion.

arXiv:1907.08613Physical review. B./Physical review. BJan 13, 202012 citations

Interacting Dirac Fermions in (3+1) Dimensions

Hiroki Isobe

Springer thesesJan 1, 20170 citations

Quantum Criticality of

3+1

-dimensional massless Dirac fermions

z

) and correlation length exponent ($\ensuremath{\nu}$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field-theoretical analysis.

3d

interacting topological insulator, and it is described by two

(3+1)d

massless Dirac fermions in the infrared limit; the second example occurs in a

3d

topological superconductor, and it is formally described by only one

(3+1)d

massless Dirac fermion.