Hidden magnetism in periodically modulated one dimensional dipolar fermions

Fazzini, Serena; Montorsi, Arianna; Roncaglia, Marco; Barbiero, Luca

doi:10.1088/1367-2630/aa9037

Cited by 22 publications

(18 citation statements)

References 79 publications

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“…Their experimental realization could be relevant for technological achievements since, from one side, symmetry-protected topological orders have been proposed as ideal candidates towards the realization quantum devices like quantum repeaters [38] and substrate for measurementbased quantum computation [39] while, from the other, side Motzkin paths may have applications in the field of polymer absorption [40]. Finally we underline that, in future works, it would be very interesting to study the gapped regimes in the fermionic version of the s = 3/2 Fredkin model where exotic Haldane regimes can take place [41]. Note added: After the submission of this paper, two papers appeared on arXiv where a Motzkin spin chain is considered introducing a field theory approach to study certain observables and entanglement measures [42].…”

Section: Pacs Numbersmentioning

confidence: 87%

Haldane topological orders in Motzkin spin chains

et al. 2017

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Motzkin spin chains are frustration-free models whose ground-state is a combination of Motzkin paths. The weight of such path contributions can be controlled by a deformation parameter t. As a function of the latter these models, beside the formation of domain wall structures, exhibit gapped Haldane topological orders with constant decay of the string order parameters for t < 1. A behavior compatible with a Berezinskii-KosterlitzThouless phase transition at t = 1 is also presented. By means of numerical calculations we show that the topological properties of the Haldane phases depend on the spin value. This allows to classify different kinds of hidden antiferromagnetic Haldane gapped regimes associated to nontrivial features like symmetry-protected topological order. Our results from one side allow to clarify the physical properties of Motzkin frustration-free chains and from the other suggest them as a new interesting and paradigmatic class of local spin Hamiltonians. [6] has been discovered for spin-1 XXZ Heisenberg chains. This has driven significant efforts to look for new kinds of models whose topological order can be described in terms of a SOP [7] motivating the discovery of the celebrated AffleckKennedy-Lieb-Tasaki (AKLT) model [8]. Although the argument of Haldane is given for integer spin chains, only integer spin XXZ-like and AKLT-like chains own topological HP and is therefore non-trivial to find and study new classes of Hamiltonians where HP emerges. Thanks to the strongest quantum "resource", namely the entanglement, spin models have also a fundamental role in the simulation of quantum logical gates for quantum computation [4]. For this reason finding and studying Hamiltonians with highly entangled spins is currently one of the most challenging and intriguing fields in quantum physics. In this direction local integer frustration-free spin Hamiltonians whose ground-state can be expressed as a combination of Motzkin paths [9] have been recently introduced [10,11]. Among others interesting aspects, their importance is given by the fact that they own a level of entanglement entropy which strongly exceeds the one exhibited by other previously known local models. Relevantly, also for half-integer spins, a similar class of Hamiltonians, the Fredkin spin chains, exhibiting the same features [12,13] has been introduced. In addition to their entanglement properties Motzkin chains own further very peculiar properties. Indeed, even if they are purely local models, for high spin values s (i.e., s ≥ 2) they behave as de facto long range Hamiltonians being able to violate cluster decomposition properties (CDP) and area law (AL) scaling DMRG local magnetization for a system of length 2n = 60 at different t deformation values S z i for c) s = 1 and d) s = 2. Lower panels: Thermodynamic limit of the gap ∆ = E1 − E0 as a function of t for e) s = 1 (red circles) and f) s = 2 (blue squares). The continuos lines are fitted with the form ∼ exp(−b/ √ tc − t) with tc = 1 and b a fitting parameter. The thermodynamic limit ...

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Section: Pacs Numbersmentioning

confidence: 87%

Haldane topological orders in Motzkin spin chains

et al. 2017

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“…1. Also, phases characterized by a non-vanishing C ν S , see for instance [19], are symmetry protected topological (SPT [32]) phases [23] with non trivial topological properties, like the presence of degenerate edge modes. Whereas phases with non-vanishing C ν P are trivial SPT phases.…”

Section: Non-local Order Parametersmentioning

confidence: 99%

“…1, the phase digram of the EFM presents a large variety of phase transitions, namely KT, gaussian and first order. As shown for instance in [19], this latter kind is usually not captured by standard bosonization approaches. For this reason we perform quasi-exact DMRG simulations which are efficiently able to detect any kind of phase transition.…”

Section: Phase Transitionsmentioning

confidence: 99%

Non-local order parameters as a probe for phase transitions in the extended Fermi-Hubbard model

Barbiero

Fazzini

Montorsi

2017

Eur. Phys. J. Spec. Top.

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Abstract. The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local operators related to charge and spin fluctuations. The main advantage in using them is that, in contrast to usual local operators, their asymptotic average value is finite only in the appropriate gapped phases. This makes them powerful and accurate probes to detect quantum phase transitions. Our results indeed confirm that they are able to properly capture both the nature and the location of the transitions. Relevantly, this happens also for conducting phases with a spin gap, thus providing an order parameter for the identification of superconducting and paired superfluid phases.

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“…We consider a balanced unit density two-component dipolar Fermi mixture. Once these particles are trapped in a one dimensional lattice, an accurate description of the system is given by the following Hamiltonian [5]…”

Section: The Modelmentioning

confidence: 99%

“…The possibility to cool down both fermionic and bosonic atomic gases to very low temperature and to trap them onto optical lattices, together with the ability to tune the interactions and the dimensionality with high accuracy, has allowed to simulate a great variety of interacting many-body lattice Hamiltonians [2]. Particular theoretical efforts have been devoted to identifying fermionic Hubbard-like systems [3,4,5] which ground state exhibits exotic [6] and topological phases [7], described by string-like order parameters [8]. Also particles with dipolar long range interaction like polar molecules and magnetic atoms [9] are currently available in laboratories.…”

Section: Introductionmentioning

confidence: 99%

Low energy quantum regimes of 1D dipolar Hubbard model with correlated hopping

Fazzini

Barbiero

Montorsi

2017

J. Phys.: Conf. Ser.

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We apply the bosonization technique to derive the phase diagram of a balanced unit density two-component dipolar Fermi gas in a one dimensional lattice geometry. The considered interaction processes are of the usual contact and dipolar long-range density-density type together with peculiar correlated hopping terms which can be generated dynamically. Rigorous bounds for the transition lines are obtained in the weak coupling regime. In addition to the standard bosonization description, we derive the low energy phase diagram taking place when part of the interaction is embodied non-perturbatively in the single component Hamiltonians. In this case the Luttinger liquid regime is shown to become unstable with respect to the opening of further gapped phases, among which insulating bond ordered wave and Haldane phases, the latter with degenerate edge modes. arXiv:1701.08441v3 [cond-mat.str-el]

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Hidden magnetism in periodically modulated one dimensional dipolar fermions

Cited by 22 publications

References 79 publications

Haldane topological orders in Motzkin spin chains

Haldane topological orders in Motzkin spin chains

Non-local order parameters as a probe for phase transitions in the extended Fermi-Hubbard model

Low energy quantum regimes of 1D dipolar Hubbard model with correlated hopping

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