Study of the phase diagram of the Kitaev-Hubbard chain

Mahyaeh, Iman; Ardonne, Eddy

doi:10.1103/physrevb.101.085125

Cited by 22 publications

(27 citation statements)

References 49 publications

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“…While the energy and its first derivative are smooth within our precision, the second order derivative is smooth in the L and the R phases but quite fluctuating and spiky within the M phase. This may be related to the presence of fluctuations as it was recently observed in the incommensurate phase of the Kitaev-Hubbard model [49]. For the phase transitions at n = 1 between the M phase and G phase we performed a scaling analysis.…”

Section: The Transitions To the M Phasementioning

confidence: 92%

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

2020

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We study a tight binding model of \mathbb{Z}_3ℤ3-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge \boldsymbol{c=2}𝐜=2, and two gapless phases with central charge \boldsymbol{c=1}𝐜=1. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

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Section: The Transitions To the M Phasementioning

confidence: 92%

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

2020

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Section: The Transitions To the M Phasesupporting

confidence: 53%

“…Therefore, the transition follows a power law in the vicinity of 𝑈 𝑐 = −1 (see, eg, References [62,220] for a similar line of argument),…”

Section: Potts Transition In the Vicinity Of 𝐶mentioning

confidence: 80%

Exotic phases in strongly correlated parafermion chains

Wouters¹

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List of publications viib This is by no means a complete discussion of topological systems. Only the necessary background is presented for understanding 1D topological chains, as they are the protagonist of this thesis. c For the explicit form of the Hamiltonian, see Chapters 2 and 3. 2 Exact ground states for interacting Kitaev chains This chapter is based on: J. Wouters, H. Katsura and D. Schuricht, Exact ground states for interacting Kitaev chains, Physical Review B 98(11), 155119 (2018). J.W. performed most of the calculations and all numerical simulations, discussed the results and contributed to the final version of the manuscript.We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system sizes. We present analytical results for the strong Majorana zero modes, the phase diagram and the topological order. Furthermore, we generalise our results to include interactions.

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“…In this form, the model has, for example, been discussed in Refs. [66,[78][79][80]. While the structure of the phase diagram remains the same, the physical interpretation of the various phases changes.…”

Section: Next-nearest Neighbor Transverse Ising Model and Its Dualmentioning

confidence: 99%

“…In particular, the paramagnetic phase becomes a topological phase with two ground states distinguished by parity. With the Jordan-Wigner transformation from {τ x,y,z i } to fermionic operators [81], H tI becomes the Kitaev-Hubbard chain [80].…”

Section: Next-nearest Neighbor Transverse Ising Model and Its Dualmentioning

confidence: 99%

Eigenstate entanglement scaling for critical interacting spin chains

Miao

Barthel

2022

Quantum

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With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.

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Study of the phase diagram of the Kitaev-Hubbard chain

Cited by 22 publications

References 49 publications

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

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

Exotic phases in strongly correlated parafermion chains

Eigenstate entanglement scaling for critical interacting spin chains

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