Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods

Abstract

Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular $S$ and $T$ matrices to study transitions in a few families of two-dimensional (2D) wavefunctions which are ${\mathbb{Z}}_N$ ($N=2\&3$) symmetric. We find that in addition to the topologically ordered phases, the modular matrices can be used to identify nontrivial SPT phases and detect transitions between different SPT phases as well as between symmetric and symmetry-breaking phases. Therefore, modular matrices can be used to characterize various types of gapped phases in a unifying way.

References in corpus (33)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Identifying Topological Order by Entanglement Entropy
• Tensor renormalization group approach to 2D classical lattice models
• Criticality, the area law, and the computational power of PEPS
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Bipartite entanglement and entropic boundary law in lattice spin systems
• On the $Z_2$ classification of Quantum Spin Hall Models
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Characterizing topological order by studying the ground states of an infinite cylinder
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Entanglement renormalization and topological order
• Quantum simulation of 2d topological physics using orbital-angular-momentum-carrying photons in a 1d array of cavities
• Resonating valence bond states in the PEPS formalism
• Explicit tensor network representation for the ground states of string-net models
• Entanglement entropy of critical spin liquids
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• Exact entanglement renormalization for string-net models
• Chiral topological spin liquids with projected entangled pair states
• Chiral projected entangled-pair state with topological order
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Symmetry-protected topologically ordered states for universal quantum computation
• Construction and Field Theory of Bosonic Symmetry Protected Topological states beyond Group Cohomology
• Identifying quantum phases from injectivity of symmetric matrix product states
• Tensor-product representations for string-net condensed states

Cited by in corpus (22)

• Lecture Notes of Tensor Network Contractions
• Loop optimization for tensor network renormalization
• Quantum criticality under decoherence or weak measurement
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Symmetry protected topological phases under decoherence
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Entanglement entropy of (3+1)D topological orders with excitations
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Holographic encoding of universality in corner spectra
• Phase transitions of a 2D deformed-AKLT model
• Non-local Order Parameters and Quantum Entanglement for Fermionic Topological Field Theories
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Detection of 2D SPT Order with Partial Symmetries
• Twisted quantum doubles are sign problem-free