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The canonical Gross-Neveu model for $N$ two-component Dirac fermions in $2+1$ dimensions suffers a continuous phase transition at a critical interaction $g_{c1} \sim 1/N$ at large $N$, at which its continuous symmetry $\text{SO}(2N)$ is…
We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that…
Nodal-line semimetals (NLSMs) harbor a variety of novel physical properties owing to the particularities of the band degeneracies that characterize the spectrum of these materials. In symmetry-enforced NLSMs, band degeneracies, being…
We study the effect of quenched disorder on the semimetal-superconductor quantum phase transition in a model of two-dimensional Dirac semimetal with $N$ flavors of two-component Dirac fermions, using perturbative renormalization group…
Rotational misalignment of two stacked honeycomb lattices produces a moir\'e pattern that is observable in scanning tunneling microscopy as a small modulation of the apparent surface height. This is known from experiments on highly-oriented…
Hexagonal Kagome lattice is a multiband system with a quadratic band crossing point, in contrast with honeycomb lattice with linear band crossing point, which has exotic correlated effect and can produce various novel quantum states. Here…
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…
The recent experimental observations of designer Dirac Fermions and topological phases in molecular graphene are addressed theoretically. Using scattering theory we calculate the electronic structure of finite lattices of scattering centers…
We use the determinant Quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\pi$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac…
For a lattice regularized chiral-invariant $SU(2)_L\times~SU(2)_R$ fermion-scalar model with a Yukawa coupling $y$ and a Wilson-Yukawa coupling $w$, we investigate the phase structure and in particular show the existence of the…
The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=i\theta T /2$ with the "topological" angle $\theta$ and temperature $T$ was investigated numerically. In order to treat such a complex-valued…
We study theoretically the multicritical phenomena of the superconductivity (SC) and antiferromagnetism (AF) in organic conductors $\kappa$-BEDT salts. The phase diagram and the experimental data on the NMR relaxation rate $1/T_1$ is…
We construct and study the relativistic Gross-Neveu-Yukawa field theory for the $\text{SO}(2N)$ real symmetric second-rank tensor order parameter coupled to $N_f$ flavors of $4N$-component Majorana fermions in 2+1 dimensions. Such a tensor…
We investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and…
We show that several distinct broken-symmetry phases in a spin-1/2 anti-ferromagnet on a square lattice with easy-plane anisotropy, including valence bond solid, chiral spin liquid, and the XY-ordered state, can all be accessed by…
We use Grassmann algebra to study the phase transition in the two-dimensional ferromagnetic Blume-Capel model from a fermionic point of view. This model presents a phase diagram with a second order critical line which becomes first order…
We study theoretically many-body equilibrium magnetic phases and corresponding thermodynamic characteristics of ultracold three-component fermionic mixtures in optical lattices described by the SU(3)-symmetric single-band Hubbard model. Our…
The results of the simulations by Monte Carlo method of graphene with structural defects are presented. The calculations are performed within an effective quantum field theory with non-compact $3\hm + 1$--dimensional Abelian gauge field and…
We study the transport properties of a tight-binding model of non-interacting fermions with random hopping on the honeycomb lattice. At the particle-hole symmetric chemical potential, the absence of diagonal disorder (random onsite…
The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over…