Strings, Projected Entangled Pair States, and variational Monte Carlo methods

Abstract

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in Quantum Information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational abgorithm which extends DMRG to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body sytems.

4 pages. v2: Submitted version, containing more numerical data. Changed title and renamed "string states" to "string-bond states" to comply with PRL conventions. v3: Accepted version, Journal-Ref. added (title differs from journal)

References in corpus (13)

• Fault-tolerant quantum computation by anyons
• The density-matrix renormalization group
• Efficient simulation of one-dimensional quantum many-body systems
• String-net condensation: A physical mechanism for topological phases
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• Valence Bond Solids for Quantum Computation
• The computational complexity of PEPS
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Solving Gapped Hamiltonians Locally
• Entropy and Entanglement in Quantum Ground States
• Variational quantum Monte Carlo simulations with tensor-network states
• Ground state approximation for strongly interacting systems in arbitrary dimension

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