Quantum geometric contributions to the BKT transition: Beyond mean field theory

Wang, Zhiqiang; Chaudhary, Gaurav; Chen, Qijin; Levin, K.

doi:10.1103/physrevb.102.184504

Cited by 35 publications

(13 citation statements)

References 87 publications

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“…For instance, Berry curvature governs the anomalous transport of an electron wave packet [3], while its integral over the Brillouin zone (BZ) gives the Chern number, which, among other topological invariants, is central in explaining the quantum Hall effect and topological insulators [4][5][6][7][8][9]. The importance of the quantum metric for phenomena such as superconductivity [10][11][12][13], orbital magnetic susceptibility [14,15], and light-matter coupling [16] has been understood only recently, and the interest in the quantum metric is rapidly growing [17][18][19][20]. Quantum geometric concepts have also been proposed for bosonic systems composed of light, bosonic atoms, or collective excitations [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

2021

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The quantum geometry of Bloch states fundamentally affects a wide range of physical phenomena. The quantum Hall effect, for example, is governed by the Chern number, and flat-band superconductivity by the distance between the Bloch states: the quantum metric. While understanding quantum geometry phenomena in the context of fermions is well established, less is known about the role of quantum geometry in bosonic systems where particles can undergo Bose-Einstein condensation (BEC). In conventional single-band or continuum systems, excitations of a weakly interacting BEC are determined by the condensate density and the interparticle interaction energy. In contrast to this, we discover here fundamental connections between the properties of a weakly interacting BEC and the underlying quantum geometry of a multiband lattice system. We show that, in the flat-band limit, the defining physical quantities of BEC, namely, the speed of sound and the quantum depletion, are dictated solely by the quantum geometry. We find that the speed of sound becomes proportional to the quantum metric of the condensed state. Furthermore, the quantum distance between the Bloch functions forces the quantum depletion and the quantum fluctuations of the density-density correlation to obtain finite values for infinitesimally small interactions. This is in striking contrast to dispersive bands where these quantities vanish with the interaction strength. Additionally, we show how in the flat-band limit the supercurrent is carried by the quantum fluctuations and is determined by the Berry connections of the Bloch states. Our results reveal how nontrivial quantum geometry allows reaching strong quantum correlation regime of condensed bosons even with weak interactions. This is highly relevant, for example, for polariton and photon BECs where interparticle interactions are inherently small. Our predictions can be experimentally tested with flat-band lattices already implemented in ultracold gases and various photonic platforms.

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Section: Introductionmentioning

confidence: 99%

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

2021

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“…The second Hamiltonian we study, called H II , is derived from a model that has been used to construct flat bands with nonzero Chern number and to investigate the possibility of a fractional Chern insulator [46]. The same model has also been recently exploited to understand the interplay of quantum geometry and superconducting fluctuations in the superfluid phase stiffness [60,61]. For this model we take…”

Section: Discussionmentioning

confidence: 99%

Heat-bath approach to anomalous thermal transport: effects of inelastic scattering

Wang,

Boyack,

Levin

2021

Preprint

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Section: B Role Of Band Broadeningmentioning

confidence: 99%

Bound on resistivity in flat-band materials due to the quantum metric

Mitscherling,

Holder

2021

Preprint

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The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its non-classical origin. However, within a newly developed Kubo formalism for fast relaxation, the decomposition of the dc electrical conductivity into both classical (intraband) and quantum (interband) contributions recently revealed that the interband part is proportional to the quantum metric. Here, we show that interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity for semimetals at charge neutrality and for systems with highly quenched bandwidth. This is true in particular for topological flat band materials of nonzero Chern number, where an upper bound exists for the resistivity due to the common geometrical origin of quantum metric and Berry curvature. We suggest to search for these effects in highly tunable rhombohedral trilayer graphene flakes.

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Quantum geometric contributions to the BKT transition: Beyond mean field theory

Cited by 35 publications

References 87 publications

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

Heat-bath approach to anomalous thermal transport: effects of inelastic scattering

Bound on resistivity in flat-band materials due to the quantum metric

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