Quantum phase transition of the one-dimensional transverse-field compass model

Sun, Kewei; Chen, Qing-Hu

doi:10.1103/physrevb.80.174417

Cited by 39 publications

(25 citation statements)

References 53 publications

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“…It would be very interesting to be able to generalize further this study to other topological codes [65][66][67][68][69][70][71] coupled to thermal baths by deriving appropriate master equations for them. Other challenges in this direction are to study thermal effects with non-abelian topological codes [72][73][74][75][76][77][78], higher dimensional codes [12,[79][80][81][82][83][84][85][86][87][88][89] and systems with topological order based on two-body interactions [90][91][92][93], instead of many-body interactions in the Hamiltonian. This would facilitate the physical simulation of these topological quantum models [64,[94][95][96][97][98][99][100].…”

Section: Discussionmentioning

confidence: 99%

Generalized toric codes coupled to thermal baths

2012

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We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. We find that in the case of qutrits, new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension d of the qudits. While we provide an explicit proof that the system relaxes to the Gibbs state for arbitrary qudits, we also prove that above a certain crossover temperature the qutrits' initial decay rate is smaller than the original case for qubits. Surprisingly, this behavior only happens for qutrits and not for other qudits with d > 3.3 the property of locality in error detection and correction is of great importance both theoretically and for practical implementations [12][13][14]. It is also possible to generalize these topological codes for units of quantum information based on multilevel systems known as qudits, i.e. d-level systems [15][16][17][18], and study their local stability [19]. An alternative scheme to manipulate topological quantum information is based not in the ground-state properties of the system but in its excitations [11]. These are non-Abelian anyons that can implement universal gates for quantum information [20]. However, being within the framework of topological codes based on ground state properties, it is possible to formulate new surface codes known as topological color codes (TCCs) [21] such that they have enhanced quantum computational capabilities while preserving nice locality properties [21][22][23]. TCCs in two-dimensional (2D) surfaces allow for the implementation of quantum gates in the whole Clifford group. This makes possible quantum teleportation, distillation of entanglement and dense coding in a fully topological scenario. Moreover, with TCCs in 3D spatial manifolds it is possible to implement the quantum gate π/8, thereby allowing for universal quantum computation [24,25]. Very nice applications of topological surface codes can be seen in other fields [26,27].Acting externally on topological codes, in order to cure the system from external noise and decoherence, produces benefits from the locality properties of these codes. Namely, a very important figure of merit is the error threshold of the topological code, i.e. the critical value of the external noise below which it is possible to perform quantum operations with arbitrary accuracy and time. For toric codes with qubits, the error threshold is very good, about 11% [12]. This value is obtained by mapping the process of error correction to a classical Ising model on a 2D lattice with random bonds. Interestingly enough, this type of mapping can be made more general and applied to TCCs yielding the same error threshold [28] while maintaining enhanced quantum capabilities [29,30]. These results have been confirm...

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Section: Discussionmentioning

confidence: 99%

Generalized toric codes coupled to thermal baths

2012

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“…Since each Majorana fermion has √ 2 degrees of freedom, the redundant Majorana fermions thus contribute a ground-state degeneracy of O(2 N/2 ) [49]. These degenerate ground states are vulnerable and can be totally lifted by an infinitesimal transverse field [50]. The entanglement [51][52][53][54], energy dynamics [55], and the dissipative behavior [56] of the QCM have been studied over the years.…”

Section: Extended Quantum Compass Modelmentioning

confidence: 99%

Unveiling the phase diagram of a bond-alternating spin-$\frac12$ $K$-$Γ$ chain

Luo,

Zhao,

Wang

et al. 2020

Preprint

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The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev (K) interaction and a symmetric off-diagonal Γ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bondalternating spin-1/2 gx-gy K-Γ chain by density-matrix renormalization group method where gx and gy are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane (gx > gy) and odd-Haldane (gx < gy) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped Ax and Ay phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a six-fold degenerate FMU 6 phase where all the spins are parallel to one of the ±x, ±ŷ, and ±ẑ axes in a six-site spin rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-2 spin-nematic ordering in the latter is also discussed.

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“…Based on a numerical analysis [6], the first and second order quantum phase transitions in the ground state phase diagram have been identified. The effect of a transverse magnetic field on the 1D quantum compass model is also well studied recently [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 98%

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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Quantum phase transition of the one-dimensional transverse-field compass model

Cited by 39 publications

References 53 publications

Generalized toric codes coupled to thermal baths

Generalized toric codes coupled to thermal baths

Unveiling the phase diagram of a bond-alternating spin-$\frac12$ $K$-$Γ$ chain

Multicritical Point in the One-dimensional Quantum Compass Model

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