Current carrying ground state in a bilayer model of strongly correlated systems

Capponi, Sylvain; Wu, Congjun; Zhang, Shou-Cheng

doi:10.1103/physrevb.70.220505

Cited by 30 publications

(22 citation statements)

References 25 publications

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“…To access the quantum critical behavior of the CDW transition induced by repulsions, it is desired to simulate the interacting model using fermion-sign-free QMC on lattices with relatively-large size. Nonetheless, conventional auxiliary-field QMC simulations of interacting spinless fermion model generally suffer from the fermion-sign problem because the usual strategies [37][38][39][40][41][42][43][44][45][46] employed in auxiliary-field QMC for solving fermion-sign problem of even species of fermions do not directly work. Recently, we discovered that certain interacting spinless fermion systems can be studied by fermion-sign-free QMC employing Majorana representation [1].…”

Section: The Mqmc Methodsmentioning

confidence: 99%

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

2015

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Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo method introduced by us in (Li et al 2015 Phys. Rev. B 91 241117), we investigate the quantum critical phenomena of spinless Dirac fermions at their charge-density-wave phase transitions on the honeycomb lattice having N L 2 s 2 = sites with largest L = 24. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of two (twocomponent) Dirac fermions in 2+1D: 0.45(2) η = , 0.77(3) ν = , and 0.60(3) β =, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.

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Section: The Mqmc Methodsmentioning

confidence: 99%

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

2015

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“…We rationalise these findings based on large-coupling effective theories 17 . In a related Hubbard model with both interlayer density interactions and interlayer Heisenberg exchange, a previous QMC study 18 revealed the existence of a current-carrying phase. But also therein, the sign problem confined the explorable parameter space, and the interaction range that we consider here has not be explored in that previous study.…”

Section: Introductionmentioning

confidence: 97%

Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: Application to the square lattice bilayer and honeycomb lattice

Golor

Wessel

2015

Phys. Rev. B

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We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal densitydensity interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strongcoupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.

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“…[25][26][27][28] The effect of correlations in conjunction with frustration has been investigated for models of fermions and quantum spins. 20,22,[29][30][31][32][33][34][35][36] In both cases, analogs of the CSF state are obtained as staggered current (for fermions) or gapless chiral (for spins) states. An analog of the CMI state has been found for fermions in a ladder model.…”

Section: Introductionmentioning

confidence: 99%

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

et al. 2013

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Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a 'synthetic' orbital magnetic fields, we study the "fully frustrated" Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable "chiral Mott insulator" (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wavefunction which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

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Current carrying ground state in a bilayer model of strongly correlated systems

Cited by 30 publications

References 25 publications

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: Application to the square lattice bilayer and honeycomb lattice

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

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