Many groups are now interested in combining QCD and QED on the lattice. Simulations with massless photons bring new infra-red and finite size issues. When we simulate an electrically charged hadron on the lattice we do several odd things. We create charged particles from the vacuum, violating conservation of charge. We use periodic boundary conditions, which don't allow a net outward elec ... More

Entanglement entropy provides a quantitative measure of quantum purity in a quantum system. In this work, lattice methods are used to exactly solve non-relativistic, interacting few-body systems in one dimension. Focus is placed on the time-dependent dynamics of the entanglement entropy, particularly around externally driven resonances. The entanglement entropy is found to provide a robust indicat ... More

The detection of the (semi)metal-insulator phase transition can be extremely difficult if the local order parameter which characterizes the ordered phase is unknown. In some cases, it is even impossible to define a local order parameter: the most prominent example of such system is the spin liquid state. This state was proposed to exist in the Hubbard model on the hexagonal lattice in a region bet ... More

We calculate the pressure and density equations of state of both unpolarized and polarized non-relativistic fermions at finite temperature in 1D. For attractive contact interactions, where there is no sign problem, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo, and demonstrate agreement with real Langevin. F ... More

We show how lattice Quantum Monte Carlo simulations can be used to calculate electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. We compare our results to empirical data of the Mott gap in large diameter tubes.

We investigate four-Fermi theories on 3-dimensional lattices. These are Gross-Neveu and Thirring models with a varying numbers of flavours $N_f$. These theories are renormalizable in the $1/N_f$-expansion and possess an interacting continuum limit. The Thirring models are closely related to 3-dimensional QED and serve as field-theoretic models for graphene. For sufficiently small $N_f$ they show a ... More

The Thirring model is a Four-Fermi-Theory with a current-current interaction and $U(2N_\text{f})$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a toy model to study chiral symmetry breaking. In the limit of flavour-number $N_\text{f} \to 1/2$ it is connected to the Gross-Neveau model, which shows ... More

We present first-principle lattice study of continuity conjecture in $2d$ $SU(N) \times SU(N)$ Principal Chiral Model (PCM) on $R \times S^1$ with respect to circumference $L$ of $S^1$ in the presence of $Z(N)$-preserving twist. The twist can be considered as analogous to Twisted Eguchi-Kawai reduction in lattice gauge theory. We study static correlation length and find that it exhibits a peak at ... More

Using the complex Langevin method for stochastic quantization, we implement a particle-number projection technique on the partition function of spin-1/2 fermions at finite temperature on the lattice. In this presentation, we discuss the method and show results for the free energy of polarized systems of Nup+Ndown particles in a finite volume, as well as virial coefficients of various orders.

Dirac Semimetals Na3Bi and Cd3As2 are recently discovered materials, which low energy electronic spectrum is described by two flavours of massless 3+1D fermions. In order to study low energy properties of these materials we formulated lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reprod ... More

I will present recent and ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant four-fermion interaction. As in previous studies of four-fermion and Higgs--Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without break ... More

Dirac semimetal has a massless Dirac fermion protected by discrete symmetries. Under the external magnetic field, the chiral magnetic effect shows a peculiar behavior induced by the quantum anomaly. In strong magnetic field and exact massless limit, the intra-corn transition does not occur because of the helicity conservation. In exact massless limit, the transport property is dictated by the inte ... More

The influence of lattice structure defects on phase transition phenomena was studied in framework of 2D spin model. Effective mass of defect was proposed for investigation of conformal properties of the model at critical point. The volume dependence of defect's mass at critical point and the Critical Casimir interaction of two defects were studied. It was shown that this Casimir interaction is at ... More

Universality of various fermion formulations is well established in QCD-like theories that are defined around the perturbative $g^2=0$ fixed point. These arguments do not apply for conformal systems that exhibit an infrared fixed point at non-vanishing $g^2$ coupling. We investigate the step scaling function for systems with 10 and 12 fundamental flavors using domain wall fermions and compa ... More