Transfer matrices and matrix product operators play a ubiquitous role in the field of many-
body physics. This review gives an idiosyncratic overview of applications, exact results, and …

Tensor-network states (TNS) are a promising but numerically challenging tool for simulating
two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction …

We introduce a tensor renormalization group scheme for coarse graining a two-dimensional
tensor network that can be successfully applied to both classical and quantum systems on …

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor
network without changing its geometry. The method is based on a quantitative …

We analyze the problem of extracting the correlation length from infinite matrix product states
(MPS) and corner transfer matrix (CTM) simulations. When the correlation length is …

Using the framework of infinite matrix product states, the existence of an anomalous
dynamical phase for the transverse-field Ising chain with sufficiently long-range interactions …

While standard approaches to quantum simulation require a number of qubits proportional
to the number of simulated particles, current noisy quantum computers are limited to tens of …

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer
operator in infinite-system matrix product state simulations are identical up to a global …

We study critical spin systems and field theories using matrix product states, and formulate a
scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice …

Consider the partition function of a classical system in two spatial dimensions, or the
Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice …