Quantum Phase Transition in the One-Dimensional XZ Model

Brzezicki, Wojciech; Oleś, Andrzej M.

doi:10.12693/aphyspola.115.162

Cited by 35 publications

(35 citation statements)

References 9 publications

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“…d is called holistic degeneracy in this paper, and meanwhile, it represents the minimum degeneracy of the system. Therefore, it is straightforward to conclude that the ground state of the 1D compass model is 2 N/2−1 -fold degenerate, which is identical to the result obtained by the reflection positivity technique [24] and by mapping to the quantum Ising models [19].…”

Section: Example A: 1d Compass Modelsupporting

confidence: 76%

“…At present, the compass model is known to own various symmetries [18]; hence, we naturally search a case in the compass model. Indeed, the 1D compass model [14,19] (for one's interest in recent progress, see [20][21][22]), which is also referred to as the reduced Kitaev model [23], is found to be a case of our proposition. The 1D compass model has the following Hamiltonian:…”

Section: Example A: 1d Compass Modelmentioning

confidence: 68%

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Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Fan

2018

Condensed Matter

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The Jordan-Wigner transformation plays an important role in spin models. However, the nonlocality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N − 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an antiperiodic chain of lattice fermions without redundancy when the Jordan-Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model (σxσy − σxσy) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites.

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Section: Example A: 1d Compass Modelsupporting

confidence: 76%

Section: Example A: 1d Compass Modelmentioning

confidence: 68%

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Fan

2018

Condensed Matter

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“…It is shown that the 1D quantum compass model exhibits a first-order phase transition between two disordered phases with opposite signs of certain local spin correlations. The model is also diagonalized exactly by a direct Jordan-Wigner transformation [3]. The obtained by latter approach results, confirm the existence of the first-order phase transition in the ground state phase diagram.…”

Section: Introductionsupporting

confidence: 57%

“…In particular, we consider the 1D spin-1/2 quantum compass model [1][2][3][4][5][6][7]. In fact, the quantum compass model is defined for explaining the low-temperature behavior of some Mott insulators.…”

Section: Introductionmentioning

confidence: 99%

Multicritical Point in the One-dimensional Quantum Compass Model

Aziziha¹,

Motamedifar²,

Mahdavifar³

2013

Acta Phys. Pol. B

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The one-dimensional spin-1/2 quantum compass model is considered. There is a multicritical point in the ground state magnetic phase diagram of the model. By using the Jordan-Wigner transformation the diagonalized Hamiltonian is obtained and analytic expressions for the spin-spin correlation functions are determined at the multicritical point. On the other hand, the critical exponent of the energy gap in the vicinity of the multicritical point is calculated by a practical finite size scaling approach.

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“…The one-dimensional (1D) QCM has been studied much less [11][12][13][14][15][16] . In the regions III.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the one-dimensional quantum compass model

Mahdavifar¹

2010

Eur. Phys. J. B

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The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and the spin-spin correlation functions are calculated for finite chains. Two kind of the magnetic long-range orders, the Néel and a type of the stripe-antiferromagnet, in the ground state phase diagram are identified. Based on the numerical analysis, the first and second order quantum phase transitions in the ground state phase diagram are identified.

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Quantum Phase Transition in the One-Dimensional XZ Model

Cited by 35 publications

References 9 publications

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Multicritical Point in the One-dimensional Quantum Compass Model

Numerical study of the one-dimensional quantum compass model

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