# Lattice field theory simulations of Dirac semimetals

## TL;DR

This paper uses lattice field theory simulations to analyze Dirac semimetals Na$_3$Bi and Cd$_3$As$_2$, confirming they are in the insulator phase under Coulomb interactions and exploring their phase diagram.

## Contribution

It formulates a lattice field theory approach for Dirac semimetals that reproduces low-energy physics and studies their phase diagram with volume-independent results.

## Key findings

- Na$_3$Bi and Cd$_3$As$_2$ are deep in the insulator phase.
- The lattice theory reproduces effective low-energy Dirac semimetal behavior.
- Results are volume independent, confirming previous findings.

## Abstract

In this paper the observed Dirac semimetals Na$_3$Bi and Cd$_3$As$_2$ are studied within lattice simulation. We formulate lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces low energy effective theory of Dirac semimetals. Using this lattice theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant--Fermi velocity anisotropy. Within the formulated theory the results are practically volume independent in contrast with our previous study. Our results confirm our previous finding that within the Dirac model with bare Coulomb interaction both Na$_3$Bi and Cd$_3$As$_2$ lie deep in the insulator phase.