# Regensburg 2019 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 44: Correlated Electrons: Method Development

### TT 44.7: Vortrag

### Mittwoch, 3. April 2019, 16:30–16:45, H7

**Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone** — •Thomas C. Lang and Andreas M. Läuchli — University of Innsbruck, Austria

We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with *N*=4 Dirac spinor components subject to a repulsive, local four fermion interaction in 2+1*d*. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and π-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of *U*_{c} = 6.76(1) as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents ν = 0.98(1), η_{φ} = 0.53(1), η_{ψ} = 0.18(1), β = 0.75(1). We provide evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction *U*, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.