arXiv:1509.09076 · Physical review. B./Physical review. B

Strong-coupling approach to Mott transition of massless and massive Dirac fermions on honeycomb lattice

Elaheh Adibi, Somaye Jafari

Published Feb 10, 2016• 9 citations

Abstract

Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be ${U}_{c}\ensuremath{\approx}2.38t$. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large $U$ and another with single-particle gap character at large ionic potential $\mathrm{\ensuremath{\Delta}}$. The present approach gives a critical gapless state at $U=2\mathrm{\ensuremath{\Delta}}$ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

DOI: 10.1103/physrevb.93.075122

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arXiv:1509.09076 · Physical review. B./Physical review. B

Strong-coupling approach to Mott transition of massless and massive Dirac fermions on honeycomb lattice

Elaheh Adibi, Somaye Jafari

Published Feb 10, 2016• 9 citations

arXiv HTML PDF

Abstract

t

around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be

{U}_{c}\ensuremath{\approx}2.38t

. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large

U

and another with single-particle gap character at large ionic potential

\mathrm{\ensuremath{\Delta}}

. The present approach gives a critical gapless state at

U=2\mathrm{\ensuremath{\Delta}}

at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

DOI: 10.1103/physrevb.93.075122

Related papers

The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

Johann Ostmeyer, Evan Berkowitz, Stefan Krieg +3 more

The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $\nu=1.181(43)$ and $\beta= 0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $\nu=1.181(43)$ and $\beta= 0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.

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Igor N. Karnaukhov, Kateryna Levchuk, Igor N. Dubinski

We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$ -field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~ $U_c$ . $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~$U_c$. $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

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Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction Uc, then increases upturn. At Uc, there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction Uc, then increases upturn. At Uc, there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.

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In the binary alloy with composition ${A}_{x}{B}_{1\ensuremath{-}x}$ of two atoms with ionic energy scales $\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\Delta}}$, an apparent Anderson insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard $U$ to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction $U$ , the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard $U$ . Upon further increase in $U$ , again the AI phase emerges, which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction. The randomness takes advantage of such suppression and localizes the quasiparticles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator. We construct the phase diagram of this model in the plane of $(U,\mathrm{\ensuremath{\Delta}})$ for various compositions $x$ .In the binary alloy with composition ${A}_{x}{B}_{1\ensuremath{-}x}$ of two atoms with ionic energy scales $\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\Delta}}$, an apparent Anderson insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard $U$ to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction $U$, the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard $U$. Upon further increase in $U$, again the AI phase emerges, which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction. The randomness takes advantage of such suppression and localizes the quasiparticles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator. We construct the phase diagram of this model in the plane of $(U,\mathrm{\ensuremath{\Delta}})$ for various compositions $x$.

arXiv:1810.02505Physical review. B./Physical review. BJan 7, 20195 citations

Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

Zhichao Zhou, Da Wang, Zi Yang Meng +2 more

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled $\mathrm{SU}(2N)$ Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled $\mathrm{SU}(2N)$ Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.

arXiv:1512.03994Physical review. B./Physical review. BJun 29, 201669 citations

t

{U}_{c}\ensuremath{\approx}2.38t

. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large

U

and another with single-particle gap character at large ionic potential

\mathrm{\ensuremath{\Delta}}

. The present approach gives a critical gapless state at

U=2\mathrm{\ensuremath{\Delta}}

at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.

U_c=3.835(14)

as well as the critical exponents

\nu=1.181(43)

and

\beta= 0.898(37)

which are expected to fall into the

SU(2)

Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.

k

and

k+π

are coupled via the effective

λ

-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~

U_c

U_c=3.904

and

U_c=5.125

are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

U

for the Hubbard model on the honeycomb lattice. However, an understanding of the fate of the antiferromagnetic Mott insulator when holes are doped into the system is still lacking. In this work, by calculating the local spin and charge density for width-4 cylinders with DMRG, we discover a half-filled stripe order in the doped Hubbard model on the honeycomb lattice. We also perform complementary large-scale mean-field calculations with renormalized interaction strength. We observe half-filled stripe order and find stripe states with filling close to one half are nearly degenerate in energy.

U

to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction

U

, the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard

U

. Upon further increase in

U

, again the AI phase emerges, which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction. The randomness takes advantage of such suppression and localizes the quasiparticles of the metallic phase. The ultimate destiny of the system at very large

U

is to become a Mott insulator. We construct the phase diagram of this model in the plane of $(U,\mathrm{\ensuremath{\Delta}})$ for various compositions

x

\mathrm{SU}(2N)

Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.