Mott transition and dimerization in the one-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>SU</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>Hubbard model

Buchta, K.; Legeza, Örs; Szirmai, E.; Sólyom, J.

doi:10.1103/physrevb.75.155108

Cited by 46 publications

(57 citation statements)

References 30 publications

(31 reference statements)

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“…In fact, gap opens in the spectrum of all modes for U > 0 [8]. Even more interestingly, the translational symmetry of the Hamiltonian is broken and a spatially nonuniform ground state emerges whose periodicity depends on the filling.…”

Section: Theorymentioning

confidence: 99%

“…In this paper we will further analyze the physics of the SU(n) Hubbard model for commensurate fillings on the basis of our earlier works [6][7][8]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…A natural candidate for the description of such systems from the theoretical point of view is the SU(n)-symmetric generalization of the standard SU(2) Hubbard model [2] which has been investigated intensively in the past by both analytic and numerical approaches [1,[3][4][5][6][7][8][9][10]. In fact, this model may mimic strongly correlated electron systems where the orbital degrees of freedom of d and f electrons play important role and these extra degrees of freedom are taken into account by considering n-component fermions.…”

Section: Introductionmentioning

confidence: 99%

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The Role of the Exchange Interaction in the One-Dimensional n-Component Hubbard Model

2009

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The commensurate p/q-filled n-component Hubbard chain was investigated by bosonization and high-precision density-matrix renormalization-group analysis. It was found that depending on the relation between the number of components n, and the filling parameter q, the system shows metallic or insulating behavior, and for special fillings bond-ordered (dimerized, trimerized, tetramerized etc.) ground state develops in the insulating phase. A mean--field analysis shows that this bond ordering is a direct consequence of the spin-exchange interaction, which plays a crucial role in the one-parameter Hubbard model -not only for infinite Coulomb repulsion, but for intermediate values as well.

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Section: Theorymentioning

confidence: 99%

“…In this paper we will further analyze the physics of the SU(n) Hubbard model for commensurate fillings on the basis of our earlier works [6][7][8]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Role of the Exchange Interaction in the One-Dimensional n-Component Hubbard Model

2009

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“…Indeed, SU (M ) symmetric spin models have interesting phases and phase transitions, [9][10][11][12][13][14][15][16] as do Hubbard models with SU (M ) symmetry. [17][18][19][20] Several theoretical [21][22][23][24][25][26][27][28] and experimental [29][30][31][32][33][34][35] works have explored physics of cold atomic systems with SU (M ) symmetry. Some of experimentally realized SU (M ) systems are 6 Li(M = 4) [36], 173 Y b (M = 6) [32,35,37], and 87 Sr(M = 10).…”

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confidence: 99%

Baryon squishing in synthetic dimensions by effectiveSU(M)gauge fields

2015

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We investigate few body physics in a cold atomic system with synthetic dimensions (Celi et al., PRL 112, 043001 (2014)) which realizes a Hofstadter model with long-ranged interactions along the synthetic dimension. We show that the problem can be mapped to a system of particles (with SU (M ) symmetric interactions) which experience an SU (M ) Zeeman field at each lattice site and a non-Abelian SU (M ) gauge potential that affects their hopping from one site to another. This mapping brings out the possibility of generating non-local interactions (interaction between particles at different physical sites). It also shows that the non-Abelian gauge field, which induces a flavororbital coupling, mitigates the "baryon breaking" effects of the Zeeman field. For M particles, the SU (M ) singlet baryon which is site localized, is "deformed" to be a nonlocal object ("squished" baryon) by the combination of the Zeeman and the non-Abelian gauge potential, an effect that we conclusively demonstrate by analytical arguments and exact (numerical) diagonalization studies. These results not only promise a rich phase diagram in the many body setting, but also suggests possibility of using cold atom systems to address problems that are inconceivable in traditional condensed matter systems. As an example, we show that the system can be adapted to realize Hamiltonians akin to the SU (M ) random flux model. Celi et al. [38] proposed the concept of "synthetic dimensions" which achieves the goal of realizing finite sized "strip" of a Hofstadter model. Their idea, illustrated in Fig. 1, involves atoms with M internal states (labeled 1 . . . γ) in a 1D (this can also be in higher dimensions) optical lattice. The hopping of the atoms from a site j (with coordinate x j = jd, d is the spacing of the optical lattice) to its neighbour does not change its internal state, and the amplitude t is independent of γ. The internal states at a site j are now coherently coupled such that an atom in state γ at site j can "hop" to the state γ + 1 at j with an amplitude Ω j γ . This produces, as shown in Fig. 1, a square lattice strip of finite width with M sites along the "synthetic dimension". Since the coherent coupling is produced by a light of wavenumber k , we have Ω Another interesting aspect of the problem is that the SU (M ) symmetric interactions between the atoms at a site j manifest as "infinite-ranged" (distanceindependent) interactions along the synthetic dimension. For example, two atoms at site j (see Fig. 1) with γ = 1 and γ = 2 will interact with the same strength as γ = 1 and γ = 4(M ). It is the physics of such a system that is the subject of this paper, i. e., to understand interplay between the flux p/q and the SU (M ) interactions. It is essential to focus, as we do, on the physics of few particles since it provides crucial insights into constructing a many body phase diagram of the system. Previous studies [23,[25][26][27] of fermionic atoms with attractive SU (M )-interactions in a simple 1d lattice (no flux, i. e., p q = 0, Ω γ =...

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“…In the vicinity of the SU (4) point, without magnetic field, a unique gapped phase with spontaneously doubled lattice constant and dimer order (spin Peierls) is realized [16,17]; it has an order parameter…”

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confidence: 99%

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

2013

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Under the influence of an external magnetic field and spin-changing collisions, the band insulator state of one-dimensional s-wave repulsively interacting four-component fermions at half-filling transforms into Mott insulator states with a spontaneously doubled unit cell: a dimerized state for shallow lattices and a Néel state for deep lattices via an intermediate topological state. These Mott insulator phases could be of special interest for experiments as they can be reached starting from band insulator state and changing magnetic field adiabatically. [3,4]. At sufficiently low temperatures the MI phase should acquire a magnetic Néel (antiferromagnetic) ordering. Still it has not been resolved [5]; the main obstacle is the absence of efficient cooling methods in the presence of an optical lattice [6].By increasing the number of components above two, an interesting possibility of hosting exotic ground states like 2D spin liquids [7,8] or 1D topological states [9,10] emerges. A novel ingredient in multicomponent alkali-metal gases, different from the two-component case, is the presence of spin-changing collisions: two interacting atoms cannot only exchange their initial internal hyperfine states, but they can also change them to new values. The spin-changing collisions open a fascinating prospect to arrive at unconventional MI ground states of multicomponent Fermi gases starting from the band insulator (BI) state made of only two components having vanishing entropy per particle. For fermions due to the Pauli principle the minimal number of components required for BI to MI transformation is four.In this work we present the ground-state phases of fourcomponent alkali-metal fermions at half-filling obtained by nonperturbative analytical and numerical tools, particularly tailored for studying 1D systems. We identify various MI phases: Dimer and Néel states spontaneously break discrete lattice translational symmetry and are characterized by doubly degenerate ground state in thermodynamic limit and local order parameters; whereas singlet and a topological Haldane phase do not break any microscopic symmetry and are characterized by unique ground state and nonlocal parity and string orders, respectively. Even though these different MI phases are manifested below the ultralow temperatures, typical to the superexchange scale, the fact that one can start from the BI state and by adiabatically changing the magnetic field enter into these nontrivial states, makes the system of half-filled four-component alkali-metal fermions a particularly attractive candidate to resolve ground-state spin order in experiments on ultracold lattice gases. Note that the spin-changing collision processes, crucial for BI to MI transformations, are maximally pronounced at half-filling.Our main result, the ground-state phase diagram of four components of 40 K atoms, is presented in Fig. 1. Most importantly all states can be explored just by changing the lattice depth and strength of the external magnetic field without the need to modify the natura...

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Mott transition and dimerization in the one-dimensionalSU(n)Hubbard model

Cited by 46 publications

References 30 publications

The Role of the Exchange Interaction in the One-Dimensional n-Component Hubbard Model

The Role of the Exchange Interaction in the One-Dimensional n-Component Hubbard Model

Baryon squishing in synthetic dimensions by effectiveSU(M)gauge fields

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

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