Low-energy effective theory of the toric code model in a parallel magnetic field

Vidal, Julien; Dusuel, Sébastien; Schmidt, K. P.

doi:10.1103/physrevb.79.033109

Cited by 155 publications

(221 citation statements)

References 25 publications

(34 reference statements)

Supporting

Mentioning

195

Contrasting

Unclassified

Order By: Relevance

“…As for the end point of the firstorder transition line, our numerical result provides a potentially better estimate, compared to the result obtained in Ref. 10. System size limitations did not allow us to get enough resolution to answer the question of how the three phase transition lines merge around h z = h x = 0.34 9 , and, in particular, to verify that they all terminate at the same point.…”

Section: Discussionmentioning

confidence: 62%

“…10 and Fig. 11, which also display the series expansion results both at order 10 in the low-field limit 12 and at order 5 in the high-field limit 10 . Again, the Monte Carlo data and the series expansion result are in good agreement at low fields (approximately h z < 0.34).…”

Section: Phase Diagrammentioning

confidence: 99%

“…13, to larger system sizes. The behavior of TCM in a parallel field and/or a transverse field was also studied using several perturbative (high order) treatments [10][11][12] . The Monte Carlo algorithm developed in this paper suffers from the sign-problem in the presence of the transverse field component.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Deng²,

Prokof’ev³

2012

Phys. Rev. B

View full text Add to dashboard Cite

Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing the transition between the topological and chargecondensed phases, and sample it using continuous-time Monte Carlo simulations. The corresponding second-order transition line is obtained by finite-size scaling analysis of this order parameter. Symmetry breaking between charges and vortices along the first-order transition line is also observed, and our numerical result shows that the end point of the first-order transition line is located at h

show abstract

Section: Discussionmentioning

confidence: 62%

Section: Phase Diagrammentioning

confidence: 99%

See 1 more Smart Citation

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

Deng²,

Prokof’ev³

2012

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The topologically ordered phase is then preserved in the thermodynamic limit, and any given degree of suppression can be efficiently realized. The explicit example of the toric code Hamiltonian perturbed by magnetic fields has been well studied by Trebst et al (2007), Vidal, Dusuel, and Schmidt (2009), Tupitsyn et al (2010), and Dusuel et al (2011.…”

Section: F Zero-temperature Stabilitymentioning

confidence: 99%

Quantum memories at finite temperature

et al. 2016

View full text Add to dashboard Cite

To use quantum systems for technological applications one first needs to preserve their coherence for macroscopic time scales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. The state-of-the-art developments in this field are reviewed in an informative and pedagogical way. The main principles of self-correcting quantum memories are given and several milestone examples from the literature of two-, three-and higher-dimensional quantum memories are analyzed.

show abstract

“…First, we consider a magnetic field term h · σ, where the magnetic field h has no tranverse h y component [4,5,6], i.e., h · σ = h x σ x + h z σ z . This "Hamiltonian deformation" gives rise to a quantum critical point at which the system becomes scale invariant and local two-point correlation functions show a divergent behavior.…”

Section: Quantum Phase Transitionsmentioning

confidence: 99%

Fractionalization and Topological Order

Oshikawa¹

2010

Understanding Quantum Phase Transitions

View full text Add to dashboard Cite

In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventional one. We concentrate on a family of quantum lattice models, namely certain deformations of the toric code model, that exhibit continuous quantum phase transitions. One such deformation leads to a Lorentz-invariant transition in the 3D Ising universality class. An alternative deformation gives rise to a so-called conformal quantum critical point where equal-time correlations become conformally invariant and can be related to those of the 2D Ising model. We study the behavior of several physical observables, such as non-local operators and entanglement entropies, that can be used to characterize these quantum phase transitions. Finally, we briefly consider the role of thermal fluctuations and related phase transitions, before closing with a short overview of field theoretical descriptions of these quantum critical points.

show abstract

Low-energy effective theory of the toric code model in a parallel magnetic field

Cited by 155 publications

References 25 publications

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

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

Quantum memories at finite temperature

Fractionalization and Topological Order

Contact Info

Product

Resources

About