Destroying a topological quantum bit by condensing Ising vortices

Abstract

The imminent realization of topologically-protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbors what is known as a Z${}_2$ liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called {\it spinons}, or Ising flux vortices called {\it visons}. At zero temperature a Z${}_2$ liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum phase transition destroying the topological order. In this paper, we use quantum Monte Carlo to study a vison-induced transition from a Z${}_2$ liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is controlled by a new universality class beyond the standard Landau paradigm.

arXiv comment5 pages, 4 figures. Published version

References in corpus (33)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Topological quantum memory
• "Deconfined" quantum critical points
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• An RVB phase in the triangular lattice quantum dimer model
• Identifying Topological Order by Entanglement Entropy
• Computational Studies of Quantum Spin Systems
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Implementing a strand of a scalable fault-tolerant quantum computing fabric
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Topologically protected quantum bits from Josephson junction arrays
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Finite size effects on measures of critical exponents in d=3 O(N) models
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Critical exponents of a three dimensional O(4) spin model
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Universal Signatures of Fractionalized Quantum Critical Points
• Fault tolerant architectures for superconducting qubits
• Zero-Temperature Properties of the Quantum Dimer Model on the Triangular Lattice
• Vison states and confinement transitions of Z2 spin liquids on the kagome lattice
• Dynamics and transport of the Z_2 spin liquid: application to kappa-(ET)2Cu2(CN)3
• Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
• Quantum dimer model with extensive ground-state entropy on the kagome lattice
• Ordering in Cs2CuCl4: Is there a proximate spin liquid?
• Unconventional Quantum Critical Points
• Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations
• Crystallization of the resonating valence bond liquid as vortex condensation

Cited by in corpus (9)

• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum spin liquid in the semiclassical regime
• Gauge-theoretic origin of Rydberg quantum spin liquids
• Resonating valence bond physics is not always governed by the shortest tunneling loops
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Valence bond solid and possible deconfined quantum criticality in an extended kagome lattice Heisenberg antiferromagnet
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• $Z_3$ topological order in the quantum dimer-pentamer model
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model