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

Barbiero, Luca; Fazzini, Serena; Montorsi, Arianna

doi:10.1140/epjst/e2016-60386-1

Cited by 6 publications

(6 citation statements)

References 40 publications

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“…Recently, this model has been re-examined in light of symmetry protected topological orders [50] and a complete classification of its phases in terms of nonlocal, parity and string-like, order parameters has been given. Similar results have been obtained also for the half-filled dipolar gas chain [51], i.e. with long-range interactions decaying as the cube of the distance.…”

supporting

confidence: 83%

One-dimensional extended Hubbard model with soft-core potential

Botzung¹,

Pupillo²,

Simon³

et al. 2019

Preprint

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We investigate the T = 0 phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Dalmonte, W. Lechner, Z. Cai, M. Mattioli, A. M. Läuchli and G. Pupillo, Phys. Rev. B 92, 045106 (2015)]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge c = 5/2, along which the two (spin and charge) bosonic degrees of freedom (corresponding to c = 1 each) combine in a supersymmetric way with an emergent fermionic excitation (c = 1/2). We also demonstrate that there are no significant spin correlations.

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confidence: 83%

One-dimensional extended Hubbard model with soft-core potential

Botzung¹,

Pupillo²,

Simon³

et al. 2019

Preprint

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“…to the Hubbard model, which describes the competition of a band "hopping" term and an "on-site" two-body Coulomb repulsion with coefficient U, the model in Equations ( 1) and ( 2) is obtained, with m ν ∝ U. The same model is found for a wide class of extended Hubbard-like models that include further interaction beyond the on-site approximation, such as nearest neighbor diagonal interaction, correlated hopping, pair hopping and so on [12][13][14][15] , as well as three-and four-body interactions [6] that may be relevant in ultracold atoms or molecules trapped in optical lattices.…”

Section: Sine Gordon Hamiltonian In One Dimensionmentioning

confidence: 68%

“…While both BOW and CDW phases are fully gapped, and are thus associated to the ordering of appropriate local operators, the Mott insulating phase has no local order parameter. Remarkably, as shown in [5,14], NL operators are able to capture accurately and distinguish all three insulating regimes, as well as the transitions among them. It is thus natural to ask how including terms further than nearest neighbors in the interaction, such as in the case of dipolar or Coulomb interaction, will affect the behavior of NL operators, as well as whether they will still behave as order parameters for the three distinct phases.…”

Section: The Extended Long-range Hubbard Modelmentioning

confidence: 84%

Hidden Charge Orders in Low-Dimensional Mott Insulators

Fazzini

Montorsi

2019

Applied Sciences

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The opening of a charge gap driven by interaction is a fingerprint of the transition to a Mott insulating phase. In strongly correlated low-dimensional quantum systems, it can be associated to the ordering of hidden non-local operators. For Fermionic 1D models, in the presence of spin–charge separation and short-ranged interaction, a bosonization analysis proves that such operators are the parity and/or string charge operators. In fact, a finite fractional non-local parity charge order is also capable of characterizing some two-dimensional Mott insulators, in both the Fermionic and the bosonic cases. When string charge order takes place in 1D, degenerate edge modes with fractional charge appear, peculiar of a topological insulator. In this article, we review the above framework, and we test it to investigate through density-matrix-renormalization-group (DMRG) numerical analysis the robustness of both hidden orders at half-filling in the 1D Fermionic Hubbard model extended with long range density-density interaction. The preliminary results obtained at finite size including several neighbors in the case of dipolar, screened and unscreened repulsive Coulomb interactions, confirm the phase diagram of the standard extended Hubbard model. Besides the trivial Mott phase, the bond ordered and charge density wave insulating phases are also not destroyed by longer ranged interaction, and still manifest hidden non-local orders.

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“…We analyse the quantum correlations and many-body entanglement present in the reduced density matrices among the different phases of the model and across its quantum phase transitions. Most studies of the EHM in the quantum information context has dealt with the quantum correlations and entanglement among the modes of the system [35][36][37][38][39][40][41][42][43][44]. Here modes can be any defined set of single particle degrees of freedom, as e.g., the spatial localized degrees along the sites of the chain, or (spatially delocalized) momentum degrees of freedom for single particles.…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model

Ferreira,

Maciel,

Vianna

et al. 2021

Preprint

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We study the ground state properties of the one-dimensional extended Hubbard model at halffilling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of 2 fermions and perform an analysis of its quantum correlations and coherence along the different phases of the model. Specifically, we study its (i) entanglement entropy, (ii) 1 norm of coherence, (iii) irreducible two-body cumulant matrix and (iv) entanglement spectrum. Our results show that these different properties are complementary to each other depending on the phase of the system, exhibiting peculiar behaviors such as discontinuities, maximun or minimun values at the quantum phase transitions, thus providing a qualitative view of the phase diagram of the model. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system. Moreover, from the analysis of the dominant eigenvector in the reduced state, we can relate the SS-TS transition to the spatial separation between the fermion pairs in the two different pairing orderings.

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

Cited by 6 publications

References 40 publications

One-dimensional extended Hubbard model with soft-core potential

One-dimensional extended Hubbard model with soft-core potential

Hidden Charge Orders in Low-Dimensional Mott Insulators

Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model

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