Yi-Fan Jiang

Emergent Spacetime Supersymmetry in 3D Weyl Semimetals and 2D Dirac Semimetals.

Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidence of it has been revealed in nature yet. In this Letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using a renormalization group, we theoretically show that N=2 space-time SUSY emerges at the continuous PDW transitions in 3D Weyl semimetals, which we believe is the first realization of emergent (3+1)D space-time SUSY in microscopic lattice models. We further discuss possible routes to realize such lattice models and experimental signatures of emergent SUSY at the PDW criticality.

Fermion-induced quantum critical points

A unified theory of quantum critical points beyond the conventional Landau–Ginzburg–Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau–Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) phase transitions on the honeycomb lattice having

Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations.

N_s=2L^2

Charge-4e superconductors: a Majorana quantum Monte Carlo study

sites with largest

Edge quantum criticality and emergent supersymmetry in topological phases.

L=24

Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo

. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of {\it two} (two-component) Dirac fermions in 2+1D:

Fermion-induced quantum critical points: beyond Landau criterion

\eta=0.45(2)

Fermion-induced quantum critical points: type-II Landau-forbidden transitions

,

Emergent space-time supersymmetry in 3D Weyl semimetals and 2D Dirac semimetals

\nu=0.77(3)