Quantum Monte Carlo study of strange correlator in interacting topological insulators

Wu, Han‐Qing; He, Yuan Yao; You, Yi; Xu, Cenke; Meng, Zi Yang; Lu, ZY

doi:10.1103/physrevb.92.165123

Cited by 23 publications

(15 citation statements)

References 51 publications

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“…Recently it has been proposed that the strange correlator is able to detect short-range entangled topological states and has been successful in identifying many topological states of matter including the Haldane phase in spin-one Heisenberg antiferromagnets, 1D and 2D AKLT states, quantum spin Hall state and bosonic symmetry-protected topological state. [32,33,34,35] The virtue of strange correlator is that no bipartition of a system is involved and the finite-size effect from the open boundary calculation is heavily reduced.…”

Section: Strange Correlator In 1d P-wave Periodic Anderson Modelmentioning

confidence: 99%

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

2017

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Abstract. We have simulated a half-filled 1D p-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the p-wave Kondo lattice model, though the soluble non-interacting limit corresponds to the conventional Z2 topological insulator. The site-resolved magnetization in an open boundary system and strange correlator for the periodic boundary have been used to identify the mentioned topological states. Interestingly, the edge magnetization in the Haldane-like state is not saturated to unit magnetic moment due to the intrinsic charge fluctuation in our periodic Anderson-like model, which is beyond the description of the Kondo lattice-like model in existing literature. The finding here underlies the correlation driven topological state in this prototypical interacting topological state of matter and naive use of non-interacting picture should be taken care. Moreover, no trace of the surface Kondo breakdown at zero temperature is observed and it is suspected that frustration-like interaction may be crucial in inducing such radical destruction of Kondo screening. The findings here may be relevant to our understanding of interacting topological materials like topological Kondo insulator candidate SmB6.

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Section: Strange Correlator In 1d P-wave Periodic Anderson Modelmentioning

confidence: 99%

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

2017

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“…1). Unlike its time-reversal invariant counterpart the Kane-MeleHubbard model, which has been studied successfully by quantum Monte Carlo (QMC) methods in recent years, [20][21][22][23][24][25][26][27][28][29][30][31][32][33] the HH model breaks time-reversal symmetry, which leads to the notorious fermion sign problem and precludes the use of QMC methods. Previous studies of the HH model have thus investigated two limiting cases.…”

Section: Introductionmentioning

confidence: 99%

Quantum cluster approach to the spinful Haldane-Hubbard model

Faye

Sénéchal

et al. 2016

Phys. Rev. B

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We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial Néel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial Néel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.

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“…Here we concentrate on two U -driven TPTs, which are described by spin Chern number variation in odd or even integer across the transitions. The anisotropy introduced by the J-term inside unit cell suppresses the xy-AFM long range order, which otherwise arises in the large U limit with J = 0 [65][66][67], but favors a topologically trivial dimerized insulator phase without breaking time-reversal symmetry and spin U (1) symmetry. The Udriven TPT with spin Chern number variation |∆C s | = 1 can be realized by setting t d = t, λ = 0.2t, t 3 = 0 (green dot in Fig.…”

Section: A Interaction-driven Tpts In Gkmh Modelmentioning

confidence: 99%

Topological invariants for interacting topological insulators. II. Breakdown of single-particle Green's function formalism

Meng

et al. 2016

Phys. Rev. B

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Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series (arXiv:1510.07816), we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants constructed from the Green's function formalism in the context of symmetry protected topological (SPT) states is presented.

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Quantum Monte Carlo study of strange correlator in interacting topological insulators

Cited by 23 publications

References 51 publications

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

Quantum cluster approach to the spinful Haldane-Hubbard model

Topological invariants for interacting topological insulators. II. Breakdown of single-particle Green's function formalism

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