Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
arXiv:1710.01851 · doi:10.1016/j.nuclphysb.2017.10.004
Abstract
An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c=m/2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.
23 pages, 1 figure, 3 tables
References in corpus (9)
- Entanglement versus Correlations in Spin Systems
- Topological characterization of quantum phase transitions in a S=1/2 spin model
- Localizable Entanglement
- Identifying phases of quantum many-body systems that are universal for quantum computation
- Criticality in correlated quantum matter
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Genuine Multipartite Entanglement in the Cluster-Ising Model
- MERA for Spin Chains with Continuously Varying Criticality
- Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
Cited by in corpus (16)
- Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
- Geometric Criterion for Solvability of Lattice Spin Systems
- Onsager algebra and cluster XY-models in a transverse magnetic field
- Generalised Onsager Algebra in Quantum Lattice Models
- Onsager algebra and algebraic generalization of Jordan-Wigner transformation
- Exact solution of a cluster model with next-nearest-neighbor interaction
- Integrable spin chains and the Clifford group
- Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations
- Exact real time dynamics with free fermions in disguise
- Exactly Solvable 1D Quantum Models with Gamma Matrices
- The Yang-Baxter integrability of the critical Ising chain
- The Hilbert-space structure of free fermions in disguise
- A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
- The exact susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions
- Conserved Charges of Series of Solvable Lattice Models
- Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models