Related papers: Continuous Matrix Product States for Quantum Field…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscilator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the…
We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context.…
Continuous tensor network gives a variational ansatz for the ground state of the quantum field theories (QFTs). The notable examples are the continuous matrix product state (cMPS) and the continuous multiscale entanglement renormalization…
We propose a lattice field theory formulation which overcomes some fundamental difficulties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the…
We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of…
Exact matrix product state representations for a type of scale-invariant states are presented, which describe highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes in one-dimensional quantum…
Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural definition of the latter. The missing element is a projector in…
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented…
We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state…