Geometry-induced pair condensation

Tovmasyan, Murad; Nieuwenburg, Evert P. L. van; Huber, Sebastian

doi:10.1103/physrevb.88.220510

Cited by 86 publications

(107 citation statements)

References 33 publications

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“…For the discussion of the interacting problem below, the Wannier states form a convenient local orthonormal basis [6,28]. The Wannier function of the flat band centered at the unit cell j is constructed from the Bloch functions g kσ (α) of the flat band according to [31,32] …”

Section: A Modelmentioning

confidence: 99%

“…A prime example is the fractional quantum Hall effect [1]. Beyond the physics in a strong magnetic field, flat or nearly flat bands are a relatively common occurrence in lattice Hamiltonians where they can be realized by engineering suitable hopping matrix elements [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Given the vanishing group velocity, one could expect an electronic flat band system to be a particularly bad conductor.…”

Section: Introductionmentioning

confidence: 99%

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Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

et al. 2016

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In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Nevertheless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher-lying bands via the perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian, if a simple uniform pairing condition on the single-particle states is satisfied, and that the compressibility is diverging as a consequence of an emergent SU(2) symmetry. This symmetry is broken by second-order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality D W 2 between the Drude weight D and the winding number W, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

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Section: A Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

et al. 2016

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“…However, interactions and disorder lead to a reconstruction of the ground state whose properties are often hard to predict. Bands that are nearly flat and/or feature a nontrivial topological invariant, similar to Landau levels producing the quantum Hall effects [2][3][4], have been considered in recent theoretical works [5][6][7][8][9][10][11][12] and can be realized in ultracold gas experiments [13][14][15]. Flat-band ferromagnetism has been studied first by Lieb [16] and, subsequently, by Tasaki and Mielke [17][18][19][20].…”

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confidence: 99%

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

et al. 2016

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The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure quantity derived solely from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.

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“…two connected chains. This geometry has been extensively studied both in Josephson junctions arrays and bosonic atoms in optical lattices also in presence of interactions [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. To be highlighted is the emergence of a quantum phase transition for bosonic FIG.…”

Section: Introductionmentioning

confidence: 99%

Geometry of system-bath coupling and gauge fields in bosonic ladders: Manipulating currents and driving phase transitions

Guo¹,

Poletti²

2016

Phys. Rev. A

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Quantum systems in contact with an environment display a rich physics emerging from the interplay between dissipative and Hamiltonian terms. Here we focus on the role of the geometry of the coupling between the system and the baths. In the specific we consider a dissipative boundary driven ladder in presence of a gauge field which can be implemented with ion microtraps arrays. We show that, depending on the geometry, the currents imposed by the baths can be strongly affected by the gauge field resulting in non-equilibrium phase transitions. In different phases both the magnitude of the current and its spatial distribution are significantly different. These findings allow for novel strategies to manipulate and control transport properties in quantum systems.

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Geometry-induced pair condensation

Cited by 86 publications

References 33 publications

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

Geometry of system-bath coupling and gauge fields in bosonic ladders: Manipulating currents and driving phase transitions

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