Applications of lattice QCD techniques for condensed matter systems
arXiv:1602.08431 · doi:10.1142/S0217751X16430089
Abstract
We review the application of lattice QCD techniques, most notably the Hybrid Monte-Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a basic introduction into the HMC algorithm as applied to condensed matter systems, we review HMC simulations of graphene, which in the recent years have helped to understand the semi-metal behavior of clean suspended graphene at the quantitative level. We also briefly summarize other novel physical results obtained in these simulations. Then we comment on the applicability of Hybrid Monte-Carlo to topological insulators and Dirac and Weyl semi-metals and highlight some of the relevant open physical problems. Finally, we also touch upon the lattice strong-coupling expansion technique as applied to condensed matter systems.
20 pages, 5 figures, Contribution to IJMPA special issue "Lattice gauge theory beyond QCD". List of references updated
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Cited by in corpus (9)
- Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
- Critical behavior in the presence of an order-parameter pinning field
- Numerical evidence of conformal phase transition in graphene with long-range interactions
- Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model
- Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
- Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions
- Direct detection of metal-insulator phase transitions using the modified Backus-Gilbert method
- Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
- Spin-density wave state in simple hexagonal graphite