Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair  hopping

Mahyaeh, Iman; Wouters, Jurriaan; Schuricht, Dirk

doi:10.21468/scipostphyscore.3.2.011

Cited by 10 publications

(19 citation statements)

References 49 publications

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“…Nevertheless, it exhibits rich physics, and for n = 3 and µ m = 0 the phase diagram was obtained in Ref. [83]. Quite remarkably, the model ( 16) simplifies dramatically in the presence of dissipation, as we shortly demonstrate.…”

Section: The Modelsupporting

confidence: 67%

Free Fock parafermions in the tight-binding model with dissipation

Mastiukova¹,

Kurlov²,

Gritsev³

et al. 2022

Preprint

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Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals require unphysical conditions such as realizing purely non-Hermitian systems. Here we present a way for the realization of free Fock parafermions in the tight-binding model with controlled dissipation of a very simple form. Introducing dissipation transforms an originally non-integrable quantum model to an exactly solvable classical one.

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Section: The Modelsupporting

confidence: 67%

Free Fock parafermions in the tight-binding model with dissipation

Mastiukova¹,

Kurlov²,

Gritsev³

et al. 2022

Preprint

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“…A number of recent works have suggested the possibility of observing anyons also in one spatial dimension, within carefully engineered cold atomic setups [3][4][5][6]. These works complemented previous theoretical investigations, where different models of 1D anyonic particles were introduced [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], exhibiting intriguing features that are not present in fermionic or bosonic systems.…”

Section: Introductionmentioning

confidence: 71%

“…At leading order, one obtains [27,87] In this appendix, we provide a proof of the formula in Eq. ( 38) that has been used in the main text to evaluate the non-universal amplitudes B κ m appearing in the asymptotic expansion (25) of Ψ † κ . The starting point is the asymptotic representation of a local field Ôn (x) of our microscopic model (3) as a combination of operators φm,n (x) of the effective field theory ( 26)…”

Section: Excited States Bethe Integersmentioning

confidence: 99%

One-particle density matrix of a trapped Lieb-Liniger anyonic gas

Scopa,

Piroli,

Calabrese

2020

Preprint

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We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the nonuniversal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks-Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids, we provide exact expansions for the oneparticle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.

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“…In the following we set α = α = e − iπ 6 /sin(π/3) which lies at the mid-section between the ferromagnetic and anti-ferromagnetic phases of the model. Recent investigations of the parameter space of the system using DMRG tools offer detailed insight [16,17].…”

Section: Background a The Parafermion Chainmentioning

confidence: 99%

Universality of Z3 parafermions via edge mode interaction and quantum simulation of topological space evolution with Rydberg atoms

Benhemou¹,

Angkhanawin²,

Adams³

et al. 2021

Preprint

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Parafermions are Zn generalisations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. We study the simplest case of the Z3 parafermion chain and investigate the form of the non-topological gate that arises through direct short-range interaction of the parafermion edge modes. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, with the strongest order of the interaction generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We also illustrate the accessibility of highly non-contextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z3 topological states with Rydberg atom technology.

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Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

Cited by 10 publications

References 49 publications

Free Fock parafermions in the tight-binding model with dissipation

Free Fock parafermions in the tight-binding model with dissipation

One-particle density matrix of a trapped Lieb-Liniger anyonic gas

Universality of Z3 parafermions via edge mode interaction and quantum simulation of topological space evolution with Rydberg atoms

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