Abstract
An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a smaller bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this goal for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.
Highlights
The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator
The density matrix renormalization group (DMRG) [1,2] and quantum tensor networks [3, 4] provide algorithms for simulating ground states of strongly correlated quantum many body systems with a computational cost that scales linear in the system size, thereby overcoming the infamous exponential wall of the quantum many body problem
There are many interesting physical problems for which this bond dimension can become prohibitively large, such as the problem of simulating time evolution of a quantum state out of equilibrium or of contracting a tensor network comprised of a projected entangled pair state (PEPS) with a large bond dimension
Summary
Our main motivation is the development of efficient MPS algorithms which can deal with time-evolution methods involving MPOs with large bond dimension and of efficient and well-conditioned ways of contracting PEPS [16]. A specific instance of the above scheme occurs when applying a uniform matrix product operator (MPO) to a given MPS, and approximating the resulting state as an MPS with a certain bond dimension.
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