Quantum Monte-Carlo (QMC) simulations are an important non-pertubative
numeric method for studying physics of strongly correlated many-body
systems, which yield unbiased results at high numeric precision in the
absence of the sign-problem.
We have made significant progress in applying the sign-problem
free QMC simulations to explore various fundamental problems
of strong correlation problems, including interacting topological
insulators, doped Mott insulators, itinerant ferromagnetism and
Curie-Weiss metals, novel quantum magnetism with SU(N) symmetries.
2D topological insulators
We performed one of the two earliest QMC simulations for topological
insulators and the helical edge states. It was based on the Kane-Mele
Hubbard model and we proved that it is sign-problem free.
See
the helical edge liquid and [Ref 1.]
Curie-Weiss metal and magnetic criticality
We performed, to our knowledge, the first sign-problem free QMC
simulations on itinerant ferromagnetism and the Curie-Weiss metal
state. Magnetic criticality is explored.
See
Cuire-Weiss metal and magnetic criticality and
[Ref 2.]
Doping an Antiferromagnetic Mott Insulator
The emergence of superconductivity in the vicinity of antiferromagnetism
is a universal phenomenon frequently observed in strongly correlated
materials.
We study the transition from an antiferromagnetic insulator to a
superconductor driven by hole-doping via the projector QMC simulations
[Ref. 3] , which are sign-problem-free both at
and away from the half-filling.
It is based on a bilayer lattice model with the onsite Hubbard
interaction and intra-rung charge and spin exchange interactions.
An Ising anisotropic antiferromagnetic Mott insulating phase occurs
at half-filling, which is weakened by hole doping.
Below a critical doping value xc=0.11, the antiferromagnetism coexists
with the singlet superconductivity, which is an intra-rung pairing
with an extended s-wave symmetry.
As further increasing doping, the antiferromagnetic order vanishes,
leaving only a pure superconducting phase.
These results provide important information how superconductivity
appears upon doping the parent Mott insulating state.
Inter-layer current phase
The interlayer staggered current phase Strongly interacting
systems have been conjectured to spontaneously develop current
carrying ground states under certain conditions. However, most results in
2D are based on mean field approximations whose validity is hard to justify.
In contrast, we (with S. Capponi and S. C. Zhang) performed the QMC
simulation to an extended bilayer Hubbard model without the sign problem,
finding a commensurate staggered interlayer current phase
[Ref. 4] .
To our knowledge, it is the first work to conclusively demonstrate
the existence of such a phase in 2D.
Novel quantum magnetism of SU(2N) fermions -- Slater v.s. Mott, Dirac
fermions, new type of quantum phase transition
There exist two basic pictures for interacting insulators --
the weak coupling Slater mechanism based on Fermi surface nesting, and
the strong coupling Mott one based on local moments and super-exchange.
In the SU(2) case, the evolution between these two limits is smooth
without a quantum phase transition.
How about in the SU(2N) case?
We have found fundamentally different features by the sign-problem free
QMC based on SU(2N) Hubbard models on the square lattice
[Ref. 5] .
The AFM order appears in weak and intermediate coupling regions agreeing
with the Slater insulator picture.
However, as further increasing interaction, it becomes suppressed.
In the SU(6) case, the AFM is completely suppressed in the
strong interacting region, i.e., the Mott insulator, where
the quantum paramagnetic columnar dimer state appears.
This shows a clear quantum phase transition between the Slater and Mott
insulating regions.
We investigated the Mott-insulating state of the SU(2N) Dirac fermions
via the sign-problem free QMC simulations
[Ref. 6 ] .
It is based on the SU(2N) Hubbard model on a honeycomb lattice.
Unlike the SU(2) case, the SU(4) and SU(6) Mott-insulating phases are
identified with the columnar valence-bond-solid (cVBS) order in the
absence of the Neel ordering.
Although the Dirac semimetal-to-cVBS transitions are typically first
order due to a cubic invariance possessed by the cVBS order, the
coupling to gapless Dirac fermions can soften these transitions to the
second order at zero temperature.
Detect edge degeneracy in interacting topological insulators using entanglement entropy
The existance of degenerate or gapless edge states is a characteristic
feature of topological insulators, but is difficult to detect in the
presence of interactions.
We propose a new method to obtain the degeneracy of the edge states
from the perspective of entanglement entropy
[Ref. 7] , which is very useful
to identify interacting topological states.
Employing the determinant quantum Monte Carlo technique, we investigate
the interaction effect on two representative models of fermionic
topological insulators in one and two dimensions, respectively.
In the two topologically nontrivial phases, the edge degeneracies
are reduced by interactions but remain to be nontrivial.
References and Talks
1. Dong Zheng, Guang-Ming Zhang Congjun Wu,
"Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model",
Phys. Rev. B 84 , 205121 (2011) , see,
pdf file
.
2. Shenglong Xu, Yi Li, Congjun Wu,
"Sign-Problem-Free Quantum Monte Carlo Study on Thermodynamic Properties and Magnetic Phase Transitions in Orbital-Active Itinerant Ferromagnets",
Phys. Rev. X 5, 021032, (2015) .
3. Tianxing Ma, Da Wang, Congjun Wu,
"Doping-driven Antiferromagnetic Insulator - Superconductor Transition: a Quantum Monte Carlo Study",
arXiv:1806.03652 .
4. Sylvain Capponi, Congjun Wu, and Shou-Cheng Zhang,
"Current carrying ground state in a bi-layer model",
Phys. Rev. B 70, 220505(R) (2004),
see pdf file
.
5. Da Wang, Yi Li, Zi Cai, Zhichao Zhou, Yu Wang, Congjun Wu,
Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
Phys. Rev. Lett. 112, 156403 (2014),
See pdf file
6. Zhichao Zhou, Da Wang, Zi Yang Meng, Yu Wang, Congjun Wu ,
Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
Phys. Rev. B 93, 245157 (2016) .
See pdf file
7. Da Wang, Shenglong Xu, Yu Wang, Congjun Wu,
Detect edge degeneracy in interacting topological insulators using entanglement entropy
Phys. Rev. B 91, 115118 (2015) .
See pdf file
Talk Novel magnetism with
large spin fermion
.
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Last modified: July 15, 2007.