Chiral topological superfluids in the attractive Haldane-Hubbard model with opposite Zeeman energy at two sublattice sites

Wu, Ya-Jie; Li, Ning; Kou, Su-Peng

doi:10.1140/epjb/e2015-60412-y

Cited by 11 publications

(15 citation statements)

References 36 publications

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“…In this broad range, the momentum space mean-field theory compares favorably with the more costly and difficult MPS simulations, and the winding number provides an accurate characterization of the TI phase. For stronger interactions, the ground state becomes a Mott insulator, where, in accordance to earlier work, a non-trivial spin order may appear [14][15][16][17][18][19][20][21][22]. On account of our numerical results, we discuss a possible ultracold atom experiment that can directly simulate our model, based on previous experiments with TIs [6,7,10] and the measurement of topological properties [31].…”

Section: Introductionsupporting

confidence: 77%

“…An interesting problem is the study of how this, or other TI models, are modified by the presence of interactions, either by destroying the topologically protected phase, or by replacing it with other non-trivial phases. Some work has already been done in the field of interacting TIs, the spinless Haldane model with nearest neighbor interactions [13], the Haldane-Hubbard model with spin and on-site interactions [14][15][16][17][18][19][20][21][22][23], the Kane-Mele model [24,25], pyrochlores [26], the synthetic Creutz-Hubbard model [27] or a general TI in the context of the fractional quantum Hall effect [28].…”

Section: Introductionmentioning

confidence: 99%

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Topological phases in the Haldane model with spin–spin on-site interactions

Rubio-García¹,

García-Ripoll²

2018

New J. Phys.

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Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin-spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the noninteracting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.

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Section: Introductionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Topological phases in the Haldane model with spin–spin on-site interactions

Rubio-García¹,

García-Ripoll²

2018

New J. Phys.

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“…The interplay between band topology and Hubbard interactions, both repulsive and attractive, has been studied extensively and various phases have been predicted [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. Investigation of possible exotic phases goes beyond the scope of this work.…”

Section: Superfluid Weight In the Kane-mele-hubbard And Haldane-mentioning

confidence: 99%

Band geometry, Berry curvature, and superfluid weight

et al. 2017

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We present a theory of the superfluid weight in multiband attractive Hubbard models within the BardeenCooper-Schrieffer (BCS) mean-field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time-reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.

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“…The relevant question here is to distinguish between two scenarios: the first, in which small interactions are not able to generate new phases and their main effect is a shift of the critical curves, as found in certain 3D topological insulators [45][46][47] ; and a second one, characterized by the emergence of a novel, interaction-induced, topological phase, like the one corresponding to σ 12 = ± e 2 h , predicted for the HaldaneHubbard model in Ref. [26][27][28][29]39,40 . Regarding the longitudinal conductivity, in the absence of interactions it is equal to , for all the values of (φ, W ) on the critical lines, with the exception of the crossing points (φ, W ) = (0, 0), (π, 0), where it is equal to e 2 h π 2 (of course, away from the critical lines σ ii = 0).…”

Section: Introductionmentioning

confidence: 99%

Topological phase transitions and universality in the Haldane-Hubbard model

et al. 2016

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We study the Haldane-Hubbard model by exact Renormalization Group techniques. We analytically construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line: in particular, repulsive interactions enlarge the topologically non-trivial region. The presence of new intermediate phases, absent in the non interacting case, is rigorously excluded at weak coupling. Despite the non-trivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity are independent of the interaction, thanks to remarkable cancellations due to lattice Ward Identities. In contrast to the quantization of the transverse conductivity, the universality of the longitudinal conductivity cannot be explained via topological arguments.

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Chiral topological superfluids in the attractive Haldane-Hubbard model with opposite Zeeman energy at two sublattice sites

Cited by 11 publications

References 36 publications

Topological phases in the Haldane model with spin–spin on-site interactions

Topological phases in the Haldane model with spin–spin on-site interactions

Band geometry, Berry curvature, and superfluid weight

Topological phase transitions and universality in the Haldane-Hubbard model

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