Exotic phase diagram of a topological quantum system

Shi, Xiaojie; Chen, Yan; You, J. Q.

doi:10.1103/physrevb.82.174412

Cited by 18 publications

(29 citation statements)

References 18 publications

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“…1), and we assume these vectors are orthogonal [21]. In the present calculation, we take L k = 10 and δ = 10 −2 ; we confirmed the convergence with respect to L k and δ.…”

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confidence: 68%

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Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons

Nasu

Motome

2015

Phys. Rev. Lett.

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Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum Monte Carlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. While changing the exchange constants, the phase transition changes from continuous to discontinuous one, apparently correlated with the change in the excitations from Abelian to non-Abelian anyons. We show this coincidence by computing the topological quantities: the Chern number and the thermal Hall conductivity. In addition, we find, as a diagnostic of the chiral spin liquids, successive crossovers with multi-stage entropy release above the critical temperature, which indicates that the hierarchical fractionalization of a quantum spin occurs differently between the two regions.PACS numbers: 75.10. Kt,75.10.Jm,75.30.Et Understanding of quantum spin liquids (QSLs) in magnets, where strong quantum fluctuations suppress magnetic ordering even at the lowest temperature (T ), has been one of the most challenging subjects in strongly correlated electron systems [1,2]. Among many possible realizations of QSLs, the chiral spin liquid (CSL), in which the time reversal symmetry is broken, has attracted considerable attention in not only condensed matter physics but also quantum information. This is because it may have the excitations obeying the nonAbelian anyon statistics, which are utilized as the operators in topological quantum computing [3]. To explore this exotic state, quantum spin systems on geometrically frustrated lattices have been intensively studied thus far [4]. For instance, the possibility of CSLs has been studied theoretically in the Heisenberg model on a kagome lattice [5][6][7]. Experimentally, a possible CSL was discussed for a metallic pyrochlore compound Pr 2 Ir 2 O 7 [8].Besides the analyses of geometrically-frustrated quantum magnets, a class of the models that have the exact CSL ground states has opened a new avenue in the study of CSLs [3,9,10]. One of them was originally suggested by A. Kitaev [3] and studied in detail by H. Yao and S. Kivelson [9]. This model is a variant of the honeycomb Kitaev model, which is defined on a decorated honeycomb lattice, composed by extending each honeycomb lattice site to a triangle. The exact solution of this model shows that the ground state accommodates two different types of the CSLs accompanied with Abelian and nonAbelian anyons as the elementary excitations. Interestingly, the non-Abelian CSL has topologically nontrivial Majorana fermion bands with a chiral edge mode.Although the exact solutions for the ground states serve as good references in the exploration of CSLs, it is a crucial issue how the CSLs behave against thermal fluctuations at finite T . As the discrete chiral symmetry is broken in the ground state, one expects a phase transition to the CSL at a finite T , even in two dimensions. An ...

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“…1), and we assume these vectors are orthogonal [21]. In the present calculation, we take L k = 10 and δ = 10 −2 ; we confirmed the convergence with respect to L k and δ.…”

supporting

confidence: 68%

“…First, we compute the Chern number, which is nonzero in the topologically nontrivial CSL ground state for α < α c [9,21].…”

mentioning

confidence: 99%

Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons

Nasu

Motome

2015

Phys. Rev. Lett.

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“…Recently physical realizations of the spin-1/2 Kitaev model have been proposed in optical lattice systems [14] and in quantum circuits [15]. Variants of the model have also been studied in two dimensions [16][17][18][19][20][21][22][23][24], three dimensions [25,26] and also on quasi-one-dimensional lattices [27][28][29]. Finally, the spin-S Kitaev model has been studied in the large S limit using spin wave theory [30], and the classical version of the Kitaev model has been studied at finite temperatures using analytical and Monte Carlo techniques [31].…”

Section: Introductionmentioning

confidence: 99%

Spin-1 Kitaev model in one dimension

et al. 2010

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We study a one-dimensional version of the Kitaev model on a ring of size N , in which there is a spin S > 1/2 on each site and the Hamiltonian is J n S x n S y n+1 . The cases where S is integer and half-odd-integer are qualitatively different. We show that there is a Z2 valued conserved quantity Wn for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2 N sectors, of unequal sizes. The number of states in most of the sectors grows as d N , where d depends on the sector. The largest sector contains the ground state, and for this sector, for S = 1, d = ( √ 5 + 1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term λ n Wn, and show that this has gapless excitations in the range λ

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“…The phase diagram of this sector has been studied in several works [28,54,57,58]. Defining R = √ J 2 x + J 2 y + J 2 z and J = J x = J y = J z , the phase diagrams has the two distinct phases: For R < J the system is in a gapped ν = 0 phase that supports Abelian toric code anyons.…”

Section: A the Phase Diagram Of The Y-k Modelmentioning

confidence: 99%

“…As described above, in this phase the π -flux vortices (W p = −1 eigenvalues) bind Majorana modes and behave as non-Abelian Ising anyons. When R > 2J is satisfied, it is possible to consider nonuniform couplings J α and J α for which a distinct ν = 0 phases can be obtained [58]. However, our interest will mainly be on the phases emerging for the uniform couplings J and J .…”

Section: A the Phase Diagram Of The Y-k Modelmentioning

confidence: 99%

Kitaev spin models from topological nanowire networks

2014

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We show that networks of superconducting topological nanowires can realize the physics of exactly solvable Kitaev spin models on trivalent lattices. This connection arises from the low-energy theory of both systems being described by a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of Josephson junctions of topological nanowires it arises from localized physical Majorana modes tunneling between the wire ends. We explicitly show that an array of junctions of three wires-a setup relevant to topological quantum computing with nanowires-can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Employing properties of the latter, we show that the network can be constructed to give rise to two-dimensional collective topological states characterized by Chern numbers ν = 0, ±1, and ±2, and that defects in the array can be associated with vortex-like quasiparticle excitations. In addition we show that the collective states are stable in the presence of disorder and superconducting phase fluctuations. When the network is operated as a quantum information processor, the connection to Kitaev spin models implies that decoherence mechanisms can in general be understood in terms of proliferation of the vortex-like quasiparticles.

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Exotic phase diagram of a topological quantum system

Cited by 18 publications

References 18 publications

Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons

Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons

Spin-1 Kitaev model in one dimension

Kitaev spin models from topological nanowire networks

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