SU(3) fermions on the honeycomb lattice at 
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 filling

Chung, Sangwoo S.; Corboz, Philippe

doi:10.1103/physrevb.100.035134

Cited by 20 publications

(10 citation statements)

References 89 publications

(104 reference statements)

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“…Since the density of states at the Fermi energy diverges, Theorem 1 can be thought of as a result for a singular case. In order to establish a rigorous result for a nonsingular SU(n) Hubbard model, we consider the Hamiltonian (20). To state the theorem, let us define for Since the lowest band of Eq.…”

Section: Theorem 1 Consider the Su(n) Hubbard Hamiltonianmentioning

confidence: 99%

“…In this section, we shall prove Theorem 2. Here, we consider the model (20) with the fermion number N f = |E|. First, we rewrite the Hamiltonian H 2 as follows:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…However, the recent experimental realizations of the SU(n) Hubbard models with ultracold fermionic atoms have generated renewed theoretical interest in the study of the model at finite n (> 2). A number of studies revealed that the models can exhibit exotic phases that do not appear in the SU (2) counterpart [13][14][15][16][17][18][19][20].…”

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confidence: 99%

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Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Tamura

Katsura

2021

J Stat Phys

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We present rigorous results for the SU(n) Fermi–Hubbard models with finite-range hopping in d ($$\ge 2$$ ≥ 2 ) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU(n) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU(n) ferromagnetic when the bottom bands are sufficiently flat and the Coulomb repulsion is sufficiently large.

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Section: Theorem 1 Consider the Su(n) Hubbard Hamiltonianmentioning

confidence: 99%

“…In this section, we shall prove Theorem 2. Here, we consider the model (20) with the fermion number N f = |E|. First, we rewrite the Hamiltonian H 2 as follows:…”

Section: Proof Of Theoremmentioning

confidence: 99%

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Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Tamura

Katsura

2021

J Stat Phys

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“…Refs. [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Besides the computation of ground states, for which (i)PEPS was originally developed, significant progress has also been achieved in other applications, including the study of thermodynamic properties [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], excited states [43,44], real-time evolution [36,[45][46][47] and open systems [36,48].…”

Section: Introductionmentioning

confidence: 99%

Simulation of three-dimensional quantum systems with projected entangled-pair states

Vlaar,

Corboz

2021

Preprint

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Tensor network algorithms have proven to be very powerful tools for studying one-and twodimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because the efficient contraction of a 3D tensor network is very challenging. In this paper we develop and benchmark two contraction approaches for infinite projected entangled-pair states (iPEPS) in 3D. The first approach is based on a contraction of a finite cluster of tensors including an effective environment to approximate the full 3D network. The second approach performs a full contraction of the network by first iteratively contracting layers of the network with a boundary iPEPS, followed by a contraction of the resulting quasi-2D network using the corner transfer matrix renormalization group. Benchmark data for the Heisenberg and Bose-Hubbard models on the cubic lattice show that the algorithms provide competitive results compared to other approaches, making iPEPS a promising tool to study challenging open problems in 3D.

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confidence: 99%

Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands

Tamura,

Katsura

2020

Preprint

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We present rigorous results for the SU(n) Fermi-Hubbard models with finite-range hopping in d (≥ 2) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU(n) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU(n) ferromagnetic when the bottom bands are sufficiently flat and the Coulomb repulsion is sufficiently large. Keywords Hubbard model • Ferromagnetism • Nearly flat band 1 IntroductionRecent advances in experimental techniques have made it possible to simulate various quantum systems by using ultracold atoms in optical lattices [1,2,3,4]. Thanks to the controllability of lattice potentials and interaction strengths with high accuracy, ultracold atomic systems are expected to be a versatile tool for exploring many-body physics in strongly correlated systems. Of particular interest are multicomponent fermionic systems with alkaline earth-like atoms in cold-atom setups. Experimental realizations of such systems with SU(n) symmetric interactions have been reported in [5,6,7]. They are expected to be well described by the

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SU(3) fermions on the honeycomb lattice at 13 filling

Cited by 20 publications

References 89 publications

Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Simulation of three-dimensional quantum systems with projected entangled-pair states

Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands

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