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Matrix product state representations
The freedom in representations with and without translation symmetry are determined, derive respective canonical forms and provide efficient methods for obtaining them.
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected…
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
This work describes quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions, and uses this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.
Unifying time evolution and optimization with matrix product states
- J. Haegeman, C. Lubich, I. Oseledets, Bart Vandereycken, F. Verstraete
- Computer Science
- 21 August 2014
The time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states and a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions.
Matrix product states represent ground states faithfully
We quantify how well matrix product states approximate exact ground states of one-dimensional quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also…
Lieb-Robinson bounds and the generation of correlations and topological quantum order.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.…
Matrix product density operators: simulation of finite-temperature and dissipative systems.
We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is…
Discriminating States: the quantum Chernoff bound.
The problem of discriminating two different quantum states in the setting of asymptotically many copies is considered, and the minimal probability of error is determined, leading to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem.
Time-dependent variational principle for quantum lattices.
- J. Haegeman, J. Cirac, T. Osborne, Iztok Pižorn, H. Verschelde, F. Verstraete
- MathematicsPhysical review letters
- 4 March 2011
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary-time dynamics for infinite…
Four qubits can be entangled in nine different ways
We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This…