MERA for Spin Chains with Continuously Varying Criticality

Abstract

We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z_2 x Z_2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum Ashkin-Teller model. All three models possess a continuous one-parameter family of critical points. Along this critical line, the thermodynamic limit of these models is expected to be described by classes of c=1 conformal field theories (CFTs) of two possible types: the S^1 free boson and its Z_2-orbifold. Our numerics using MERA with explicitly enforced Z_2 x Z_2 symmetry allow us to extract conformal data for each model, with strong evidence supporting the identification of the staggered XXZ model and critical transverse field cluster model with the S^1 boson CFT, and the Ashkin-Teller model with the Z_2-orbifold boson CFT. Our first two models describe the phase transitions between symmetry protected topologically ordered phases and trivial phases, which lie outside the usual Landau-Ginsburg-Wilson paradigm of symmetry breaking. Our results show that a range of critical theories can arise at the boundary of a single symmetry protected phase.

13 pages, 11 figures, comments welcome; v2 published version

References in corpus (31)

• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Entanglement renormalization
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Matrix product states represent ground states faithfully
• Algorithms for entanglement renormalization
• Tensor network decompositions in the presence of a global symmetry
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Symmetry protected topological phases from decorated domain walls
• Symmetry-protected phases for measurement-based quantum computation
• Entanglement renormalization, scale invariance, and quantum criticality
• Ground State and Finite Temperature Lanczos Methods
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Quantum MERA Channels
• Conformal Data from Finite Entanglement Scaling
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Symmetry protection of measurement-based quantum computation in ground states
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Boundary quantum critical phenomena with entanglement renormalization
• Critical theories of phase transition between symmetry protected topological states and their relation to the gapless boundary theories
• Symmetry-protected many-body Aharonov-Bohm effect
• Non-local scaling operators with entanglement renormalization
• Gapped symmetric edges of symmetry protected topological phases
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain

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• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Lecture Notes of Tensor Network Contractions
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Algorithms for tensor network renormalization
• Entanglement renormalization and wavelets
• Hyper-invariant tensor networks and holography
• Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Anomalies and entanglement renormalization
• Conformal and chiral phase transitions in Rydberg chains
• Representation and design of wavelets using unitary circuits
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Global anomaly detection in two-dimensional symmetry-protected topological phases
• Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model
• Exact solution of a cluster model with next-nearest-neighbor interaction
• Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Quantum criticality in many-body parafermion chains
• Holographic entanglement renormalisation of topological order in a quantum liquid
• Space of initial conditions and universality in nonequilibrium quantum dynamics
• Edge Theories for Anyon Condensation Phase Transitions
• Deconfined quantum criticality in a frustrated Haldane chain with single-ion anisotropy
• Probing universal critical scaling with scan-DMRG
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Emergent criticality in a constrained boson model