Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice

Abstract

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recently discovery of absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous time quantum Monte Carlo method with worm sampling technique. We estimate the transition point $V/t=1.356(1)$ with the critical exponents $\nu =0.80(3)$ and $\eta =0.302(7)$. Compatible results for the transition point are also obtained with infinite projected entangled-pair states.

Single column, 21 pages, appendix on worm updates and π-flux lattice

References in corpus (24)

• The electronic properties of graphene
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Continuous-time Monte Carlo methods for quantum impurity models
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The ALPS project release 1.3: open source software for strongly correlated systems
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Scaling of entanglement support for Matrix Product States
• Theory of interacting electrons on the honeycomb lattice
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Density waves and Cooper pairing on the honeycomb lattice
• Spin-orbital quantum liquid on the honeycomb lattice
• Interaction effects and quantum phase transitions in topological insulators
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Asymptotic safety: a simple example
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• autoScale.py - A program for automatic finite-size scaling analyses: A user's guide
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states
• Graded Projected Entangled-Pair State Representations and An Algorithm for Translationally Invariant Strongly Correlated Electronic Systems on Infinite-Size Lattices in Two Spatial Dimensions
• Quantum phase transitions in $d-wave$ superconductors

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