Phase diagram of the toric code model in a parallel magnetic field

Wu, Fengcheng; Deng, Youjin; Prokof’ev, Nikolay

doi:10.1103/physrevb.85.195104

Cited by 72 publications

(84 citation statements)

References 21 publications

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“…Based on the numerical algorithms proposed in [14,15], we obtain the results of C h 0.37  = , which is close to the previous result h 0.34  = in [18,19]. It is worthy to note that since the toric code model only contains x s and z s terms, the direction of the external magnetic field is symmetric with respect to e x  and e z  , but is asymmetric for e x  and e z  .…”

Section: Resultssupporting

confidence: 86%

Irreducible many-body correlations in topologically ordered systems

2016

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Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.

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Section: Resultssupporting

confidence: 86%

Irreducible many-body correlations in topologically ordered systems

2016

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“…This problem has been extensively studied for the toric code which is the simplest exactly solvable model with topological protection 11 . In the presence of a magnetic field, the Z 2 topologically ordered groundstate of the toric code breaks down to a polarized phase by first-or second-order quantum phase transition according to the direction of the magnetic field [16][17][18][19][20][21][22] . The latter belongs to the 3D Ising universality class except on a special line in parameter space where a more complicated behavior is observed 21 .…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions out of aZ2×Z2topological phase

et al. 2013

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We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising interactions, using high-order series expansion and exact diagonalization. In a uniform magnetic field, we find first-order phase transitions in all field directions. In contrast, our results for the Ising interactions unveil that for strong enough Ising couplings, the Z2 × Z2 topological phase of color code breaks down to symmetry broken phases by first-or second-order phase transitions.

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“…Thus our analytical results pertain to this sector where in subsections III A, III B we consider gauge invariant perturbations to H T C that take drive the system across a quantum critical point between a topologically ordered and disordered phase. For a discussion of the critical point see [56][57][58]. The more general perturbation III C is studied numerically.…”

Section: Lmentioning

confidence: 99%

Local convertibility of the ground state of the perturbed toric code

et al. 2014

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We present analytical and numerical studies of the behaviour of the α-Renyi entropies in the Toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC) -a property called localconvertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

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Phase diagram of the toric code model in a parallel magnetic field

Cited by 72 publications

References 21 publications

Irreducible many-body correlations in topologically ordered systems

Irreducible many-body correlations in topologically ordered systems

Quantum phase transitions out of aZ2×Z2topological phase

Local convertibility of the ground state of the perturbed toric code

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