Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code

Abstract

One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by studying the phase transitions induced due to the change in the boundary conditions. We claim that these phase transitions are accompanied by broken symmetries in the excitation space and to gain further insight we analyze various signatures like the ground state degeneracy, topological entanglement entropy while introducing the open-loop operator whose expectation value effectively captures the phase transition. Further, we extend the analysis to an open quantum setup by defining effective collapse operators, the dynamics of which cool the system to different topologically ordered steady states. We show that the phase transition between such steady states is effectively captured by the expectation value of the open-loop operator.

arXiv comment16 pages, 23 figures

References in corpus (35)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Topological entanglement entropy
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• A Rydberg Quantum Simulator
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Identifying Topological Order by Entanglement Entropy
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Models for gapped boundaries and domain walls
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Variational principle for steady states of dissipative quantum many-body systems
• Boundary Degeneracy of Topological Order
• High-density quantum sensing with dissipative first order transitions
• Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
• Multicritical behavior in dissipative Ising models
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Classification of phases for mixed states via fast dissipative evolution
• Numerical study of a transition between Z2 topologically ordered phases
• Quantum contact process
• Topological Order Following a Quantum Quench
• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems
• Uncovering the non-equilibrium phase structure of an open quantum spin system
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Robustness of Topological Order in the Toric Code with Open Boundaries
• An Operational Definition of Topological Order
• A quantum phase transition from $Z_2\times Z_2$ to $Z_2$ topological order
• Topological Order and Quantum Criticality
• From effective Hamiltonian to anomaly inflow in topological orders with boundaries

Cited by in corpus (1)

• Kibble-Zurek mechanism and errors of gapped quantum phases