Integrable Model with Parafermion Zero Energy Modes

Tsvelik, A. M.

doi:10.1103/physrevlett.113.066401

Cited by 20 publications

(38 citation statements)

References 25 publications

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“…0,j 0,2 (0) . Analogously to [14][15][16] the nonlinear integral equations (2.13) can be solved iteratively in this regime: the energies (m) k of solitons are well described by their first order approximation while those of the auxiliary modes can be replaced by the asymptotic solution for |λ| → ∞, see Table I for 2 ≤ N f ≤ 5. For the other modes is obtained for m = 1, j ∈ {j 0,1 ,j 0,1 } and m = 2, j ∈ {j 0,2 ,j 0,2 } resulting in the free energy j0,m (0)) close and the degeneracy of the auxiliary modes is lifted.…”

Section: B Non-interacting Solitonsmentioning

confidence: 99%

“…Unfortunately, these lattice models do not allow to tune the anyon density. To study the transition between the low density phase of 'bare' anyons and the collective state realized at high anyon densities one can follow the approach of [14][15][16] In the present paper we extend this approach to fermions with an SO(5) spin degree of freedom. 1 Again we find that the excitations in the spin sector are massive solitons.…”

Section: Introductionmentioning

confidence: 99%

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Condensates of interacting non-Abelian SO(5)Nf anyons

Borcherding

Frahm

2019

J. High Energ. Phys.

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Starting from a one-dimensional model of relativistic fermions with SO(5) spin and U (N f ) flavor degrees of freedom we study the condensation of SO(5) N f anyons. In the low-energy limit the quasi-particles in the spin sector of this model are found to be massive solitons forming multiplets in the SO(5) vector or spinor representations. The solitons carry internal degrees of freedom which are identified as SO(5) N f anyons. By controlling the external magnetic fields the transitions from a dilute gas of free anyons to various collective states of interacting ones are observed. We identify the generalized parafermionic cosets describing these collective states and propose a low temperature phase diagram for the anyonic modes.

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Section: B Non-interacting Solitonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Condensates of interacting non-Abelian SO(5)Nf anyons

Borcherding

Frahm

2019

J. High Energ. Phys.

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“…Non-Abelian states were initially predicted in fractional quantum Hall (FQH) systems 7,[22][23][24][25][26][27] that are constrained to two spacial dimensions, and subsequently in various similar FQH-like systems in 2D 4,26,[28][29][30][31][32][33][34][35][36][37][38][39] . However, analogous states were also found to appear in various one-dimensional (1D) models [40][41][42][43][44][45][46][47][48][49][50] . Whether in 1D or 2D, non-Abelian states of matter have a global hidden order with constituent particles following a global pattern that is not associated with breaking of any symmetry.…”

Section: Introductionmentioning

confidence: 99%

Fibonacci anyon excitations of one-dimensional dipolar lattice bosons

2017

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We study a system of dipolar bosons in a one-dimensional optical lattice using exact diagonalization and density matrix renormalization group methods. In particular, we analyze low energy properties of the system at an average filling of 3/2 atoms per lattice site. We identify the region of the parameter space where the system has non-Abelian Fibonacci anyon excitations that correspond to fractional domain walls between different charge-density-waves. When such onedimensional systems are combined into a two-dimensional network, braiding of Fibonacci anyon excitations has potential application for fault tolerant, universal, topological quantum computation. Contrary to previous calculations, our results also demonstrate that super-solid phases are not present in the phase diagram for the discussed 3/2 average filling. Instead, decreasing the value of the nearest-neighbor tunneling strength leads to a direct, Berezinskii-Kosterlitz-Thouless, super-fluid to charge-density-wave quantum phase transition.

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“…Although non-Abelian states are associated with twodimensional (2D) systems, analogous states can be found in certain one-dimensional (1D) models [33][34][35][36][37][38][39][40][41]. Ultimately, * tduric1@gmail.com such 1D non-Abelian states must be braided in order to compute.…”

Section: Introductionmentioning

confidence: 99%

Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

et al. 2016

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We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.

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Integrable Model with Parafermion Zero Energy Modes

Cited by 20 publications

References 25 publications

Condensates of interacting non-Abelian SO(5)Nf anyons

Condensates of interacting non-Abelian SO(5)Nf anyons

Fibonacci anyon excitations of one-dimensional dipolar lattice bosons

Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

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