A variational method based on weighted graph states
arXiv:0706.0423 · doi:10.1088/1367-2630/9/10/361
Abstract
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.
36 pages, 13 figures
References in corpus (45)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- The density-matrix renormalization group
- Entanglement in quantum critical phenomena
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Persistent entanglement in arrays of interacting particles
- Scaling of Entanglement close to a Quantum Phase Transitions
- Efficient simulation of one-dimensional quantum many-body systems
- Measurement-based quantum computation with cluster states
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
- Quantum phase transitions
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- DMRG and periodic boundary conditions: a quantum information perspective
- Criticality, the area law, and the computational power of PEPS
- Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
- Violation of the entropic area law for Fermions
- A class of ansatz wave functions for 1D spin systems and their relation to DMRG
- Universality of Entropy Scaling in 1D Gap-less Models
- Entanglement Properties of the Harmonic Chain
- Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Cluster Algorithm for Vertex Models
- Valence Bond Solids for Quantum Computation
- Entanglement in XY Spin Chain
- Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
- Universal resources for measurement-based quantum computation
- An entanglement-area law for general bosonic harmonic lattice systems
- General entanglement scaling laws from time evolution
- Entanglement scaling in critical two-dimensional fermionic and bosonic systems
- On the entanglement entropy for a XY spin chain
- Recent Developments of World-Line Monte Carlo Methods
- The ALPS project: open source software for strongly correlated systems
- Entanglement in spin chains and lattices with long-range Ising-type interactions
- Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
- Fine-grained entanglement loss along renormalization group flows
- Entanglement, quantum phase transitions, and density matrix renormalization
- Statistics dependence of the entanglement entropy
- Comment on "Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of- Equilibrium Systems"
- Ground state approximation for strongly interacting systems in arbitrary dimension
- Computational Difficulty of Global Variations in the Density Matrix Renormalization Group
- Bragg spectroscopy of trapped one dimensional strongly interacting bosons in optical lattices: Probing the cake-structure
- Spin gases as microscopic models for non-Markovian decoherence
- Entanglement entropy and the simulation of Quantum Mechanics
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