Elective-momentum ultrasize quantum Monte Carlo method

@article{Liu2019ElectivemomentumUQ,
  title={Elective-momentum ultrasize quantum Monte Carlo method},
  author={Zi Hong Liu and Xiao Yan Xu and Yang Qi and Kai Sun and Zi Yang Meng},
  journal={Physical Review B},
  year={2019}
}
One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice model of interacting fermions, the best methodology at hand still scales with $\beta N^3$ where $\beta$ is the inverse temperature and $N$ is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated… Expand

Figures from this paper

Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition
In this paper, we study the quantum criticality of Dirac fermions via large-scale numerical simulations, focusing on the Gross-Neveu-Yukawa chiral-Ising quantum critical point (QCP) with criticalExpand
Monte Carlo Studies of Quantum Critical Metals
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantumExpand
Quantum Monte Carlo Simulation of the Chiral Heisenberg Gross-Neveu-Yukawa Phase Transition with a Single Dirac Cone.
TLDR
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 is employed. Expand
Revealing fermionic quantum criticality from new Monte Carlo techniques.
This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insightsExpand
Itinerant quantum critical point with fermion pockets and hotspots
TLDR
A state-of-the-art large-scale quantum Monte Carlo simulation technique is developed and systematically investigated the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector Q=(π,π)—a problem that resembles the Fermi surface setup and low-energy antiferromeagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non–Fermi-liquid behaviors. Expand
Quantifying the fragility of unprotected quadratic band crossing points
We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on theExpand
Nematic quantum criticality in Dirac systems
Jonas Schwab, Lukas Janssen, Kai Sun, Zi Yang Meng, 5 Igor F. Herbut, Matthias Vojta, and Fakher F. Assaad Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of ExcellenceExpand
Dynamic properties of collective excitations in twisted bilayer Graphene
  • Gaopei Pan, Xu Zhang, Heqiu Li, Kai Sun, Zi Yang Meng
  • Physics
  • 2021
Gaopei Pan,1, 2 Xu Zhang,3 Heqiu Li,4 Kai Sun,4, ∗ and Zi Yang Meng3, † 1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, BeijingExpand
Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene
Xu Zhang(张栩)1†, Gaopei Pan(潘高培)2,3†, Yi Zhang(张燚), Jian Kang(康健), and Zi Yang Meng(孟子杨)1,2* Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The UniversityExpand
Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existingExpand

References

SHOWING 1-10 OF 122 REFERENCES
Sign-Problem–Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals
TLDR
Here, it is shown that the universal low-energy theory for the onset of antiferromagnetism in a metal can be realized in lattice models, which are free from the sign problem and hence can be simulated efficiently with QMC. Expand
Critical behavior of Dirac fermions from perturbative renormalization
Gapless Dirac fermions appear as quasiparticle excitations in various condensed-matter systems. They feature quantum critical points with critical behavior in the 2+1 dimensional Gross-NeveuExpand
Quantum critical properties of a metallic spin-density-wave transition
We report on numerically exact determinantal quantum Monte Carlo simulations of the onset of spin-density wave (SDW) order in itinerant electron systems captured by a sign-problem-freeExpand
Quantum spin liquid emerging in two-dimensional correlated Dirac fermions
TLDR
It is shown, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermion and an antiferromagnetically ordered Mott insulator. Expand
Itinerant quantum critical point with frustration and a non-Fermi liquid
Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degreesExpand
Ising models of quantum frustration
We report on a systematic study of two-dimensional, periodic, frustrated Ising models with quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular andExpand
Cooper pairing in non-Fermi liquids
States of matter with a sharp Fermi surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include (i) quantum critical points associated with the onset ofExpand
Stable quantum Monte Carlo algorithm for T = 0 calculation of imaginary time Green functions
We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G ( r , τ) for Hubbard type models. We illustrate the efficiency of theExpand
Anisotropic non-Fermi liquids
We study non-Fermi-liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotationalExpand
Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis
We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interactingExpand
...
1
2
3
4
5
...