Homogeneous MERA states: an information theoretical analysis
arXiv:0901.4424 · doi:10.1103/PhysRevA.79.052314
Abstract
Homogeneous Multi-scale Entanglement Renormalization Ansazt (MERA) state have been recently introduced to describe quantum critical systems. Here we present an extensive analysis of the properties of such states by clarifying the definition of their transfer super-operator whose structure is studied within a informational theoretical approach. Explicit expressions for computing the expectation values of symmetric observables are given both in the case of finite size systems and in the thermodynamic limit of infinitely many particles.
13 pages, 5 figures
References in corpus (12)
- A class of quantum many-body states that can be efficiently simulated
- DMRG and periodic boundary conditions: a quantum information perspective
- New Trends in Density Matrix Renormalization
- Algorithms for entanglement renormalization
- Entanglement renormalization and topological order
- Entanglement renormalization, scale invariance, and quantum criticality
- Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
- Quantum MERA Channels
- Ground state approximation for strongly interacting systems in arbitrary dimension
- Unifying variational methods for simulating quantum many-body systems
- Simulation of time evolution with the MERA
- The Generalized Lyapunov Theorem and its Application to Quantum Channels
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