Interplay of local order and topology in the extended Haldane-Hubbard model

Can Shao; Eduardo V. Castro; Shijie Hu; Rubem Mondaini

doi:10.1103/physrevb.103.035125

Interplay of interactions, disorder, and topology in the Haldane-Hubbard model

Physical Review B ◽

10.1103/physrevb.104.195117 ◽

2021 ◽

Vol 104 (19) ◽

Author(s):

Tian-Cheng Yi ◽

Shijie Hu ◽

Eduardo V. Castro ◽

Rubem Mondaini

Keyword(s):

Hubbard Model ◽

And Topology

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Direct detection of metal-insulator phase transitions using the modified Backus-Gilbert method

EPJ Web of Conferences ◽

10.1051/epjconf/201817503008 ◽

2018 ◽

Vol 175 ◽

pp. 03008 ◽

Cited By ~ 5

Author(s):

Maksim Ulybyshev ◽

Christopher Winterowd ◽

Savvas Zafeiropoulos

Keyword(s):

Phase Transition ◽

Hubbard Model ◽

Order Parameter ◽

Hexagonal Lattice ◽

Monte Carlo Algorithm ◽

Alternative Methods ◽

Local Order ◽

Metal Insulator ◽

Local Order Parameter ◽

Insulator Phase Transition

The detection of the (semi)metal-insulator phase transition can be extremely difficult if the local order parameter which characterizes the ordered phase is unknown. In some cases, it is even impossible to define a local order parameter: the most prominent example of such system is the spin liquid state. This state was proposed to exist in the Hubbard model on the hexagonal lattice in a region between the semimetal phase and the antiferromagnetic insulator phase. The existence of this phase has been the subject of a long debate. In order to detect these exotic phases we must use alternative methods to those used for more familiar examples of spontaneous symmetry breaking. We have modified the Backus-Gilbert method of analytic continuation which was previously used in the calculation of the pion quasiparticle mass in lattice QCD. The modification of the method consists of the introduction of the Tikhonov regularization scheme which was used to treat the ill-conditioned kernel. This modified Backus-Gilbert method is applied to the Euclidean propagators in momentum space calculated using the hybrid Monte Carlo algorithm. In this way, it is possible to reconstruct the full dispersion relation and to estimate the mass gap, which is a direct signal of the transition to the insulating state. We demonstrate the utility of this method in our calculations for the Hubbard model on the hexagonal lattice. We also apply the method to the metal-insulator phase transition in the Hubbard-Coulomb model on the square lattice.

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Haldane insulator in the 1D nearest-neighbor extended Bose-Hubbard model with cavity-mediated long-range interactions

The European Physical Journal B ◽

10.1140/epjb/e2020-10109-3 ◽

2020 ◽

Vol 93 (6) ◽

Author(s):

Johannes Sicks ◽

Heiko Rieger

Keyword(s):

Hubbard Model ◽

Quantum Monte Carlo ◽

Nearest Neighbor ◽

Mean Field ◽

Local Order ◽

One Dimensional ◽

Hubbard Models ◽

Long Range Interactions ◽

Non Local ◽

The One

Abstract In the one-dimensional Bose-Hubbard model with on-site and nearest-neighbor interactions, a gapped phase characterized by an exotic non-local order parameter emerges, the Haldane insulator. Bose-Hubbard models with cavity-mediated global range interactions display phase diagrams, which are very similar to those with nearest-neighbor repulsive interactions, but the Haldane phase remains elusive there. Here we study the one-dimensional Bose-Hubbard model with nearest-neighbor and cavity-mediated global-range interactions and scrutinize the existence of a Haldane Insulator phase. With the help of extensive quantum Monte-Carlo simulations we find that in the Bose-Hubbard model with only cavity-mediated global-range interactions no Haldane phase exists. For a combination of both interactions, the Haldane Insulator phase shrinks rapidly with increasing strength of the cavity-mediated global-range interactions. Thus, in spite of the otherwise very similar behavior the mean-field like cavity-mediated interactions strongly suppress the non-local order favored by nearest-neighbor repulsion in some regions of the phase diagram. Graphical abstract

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