scholarly journals A study of the magnetic properties in the Hubbard model on the honeycomb lattice by variational cluster approximation

2016 ◽  
Vol 30 (23) ◽  
pp. 1650158 ◽  
Author(s):  
Atsushi Yamada
Keyword(s):  
Magnetic Properties ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Large Scale ◽  
Interaction Strength ◽  
Honeycomb Lattice ◽  
Metallic State ◽  
Cluster Approximation ◽  
Nonmagnetic Metal ◽  
Variational Cluster Approximation

Magnetic properties of the half-filled Hubbard model on the honeycomb lattice, which is a simple model of graphene, are studied using the variational cluster approximation (VCA). We found that the critical interaction strength of a magnetic transition is slightly lower than that of the nonmagnetic metal-to-insulator transition and the magnetic order parameter is already nonnegligible at the latter transition point. Thus, a semi-metallic state becomes a magnetic insulator as the interaction strength increases, and a spin liquid state characterized by a Mott insulator without spontaneously broken spatial or spin symmetry, or a state very close to that is not realized in this system. Both the magnetic and nonmagnetic metal-to-insulator transitions are of the second-order. Our results agree with recent large scale quantum Monte Carlo (QMC) simulations.

MOTT TRANSITION IN THE HALF-FILLED HUBBARD MODEL ON THE HONEYCOMB LATTICE WITHIN COHERENT POTENTIAL APPROXIMATION

2013 ◽  
Vol 27 (07) ◽  
pp. 1350046 ◽  
Author(s):  
DUC ANH LE
Keyword(s):  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Mott Transition ◽  
Coherent Potential Approximation ◽  
Honeycomb Lattice ◽  
Potential Approximation ◽  
Good Agreement

Using the coherent potential approximation, we study zero-temperature Mott transition in the half-filled Hubbard model on the honeycomb lattice. Although a pseudogap is already present for the non-interacting case, the gap will not occur until the onsite Coulomb repulsion exceeds a critical value U ≈ 3.6t, where t is the hopping integral. When increasing U/t, the density of states at the Fermi energy first goes up gradually from zero and after reaching a maximum it goes down to zero again. Our calculated critical interaction UC/t is in very good agreement with the ones obtained by quantum Monte Carlo simulation and cluster dynamical mean-field theory.

scholarly journals ORTHOGONAL DIRAC SEMIMETAL ON HONEYCOMB LATTICE

2013 ◽  
Vol 27 (07) ◽  
pp. 1361002
Author(s):  
YIN ZHONG ◽  
HONG-GANG LUO
Keyword(s):  
Hubbard Model ◽  
Transport Properties ◽  
Honeycomb Lattice ◽  
Metallic State ◽  
Spin Representation ◽  
Dirac Semimetal ◽  
Disordered Phase

Recently, a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We have extended this concept to study the slave-spin representation of Hubbard model on the honeycomb lattice. It is found that a novel gapped metallic state coined orthogonal Dirac semimetal is identified. Such state corresponds to the disordered phase of slave-spin and has the same thermal-dynamical and transport properties as Dirac semimetal but its singe-particle excitation is gapped.

scholarly journals The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Martin Bercx ◽  
Florian Goth ◽  
Johannes Stephan Hofmann ◽  
Fakher Assaad
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Kondo Lattice ◽  
Monte Carlo Algorithm ◽  
Auxiliary Field ◽  
Honeycomb Lattice ◽  
Monte Carlo Code ◽  
Single Body ◽  
Lattice Fermions

The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the SU(N)SU(N)-Hubbard-Heisenberg model. One can download the code from our Git instance at and sign in to file issues.

Finite Size Scaling in the tt'-Hubbard Model and in BCS-Reduced Hubbard Models

1998 ◽  
Vol 09 (07) ◽  
pp. 943-985 ◽  
Author(s):  
W. Fettes ◽  
I. Morgenstern
Keyword(s):  
Hubbard Model ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Interaction Strength ◽  
Finite Size ◽  
Monte Carlo Algorithm ◽  
Finite Size Scaling ◽  
Hubbard Models ◽  
Size Scaling ◽  
Wave Symmetry

With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses we propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with dx2-y2-wave symmetry).

scholarly journals Attractive Hubbard model on a honeycomb lattice: Quantum Monte Carlo study

2009 ◽  
Vol 80 (24) ◽  
Author(s):  
K. L. Lee ◽  
K. Bouadim ◽  
G. G. Batrouni ◽  
F. Hébert ◽  
R. T. Scalettar ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Honeycomb Lattice ◽  
Lattice Quantum ◽  
Attractive Hubbard Model
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