Related papers: Continuous Matrix Product States for Quantum Field…
In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyse a fine-graining renormalization…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
We describe a general procedure to give effective continuous descriptions of quantum lattice systems in terms of quantum fields. There are two key novelties of our method: firstly, it is framed in the hamiltonian setting and applies equally…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
The Kosterlitz-Thouless transition is studied from the representation of the systems's ground state wave functions in terms of Matrix Product States for a quantum system on an infinite-size lattice in one spatial dimension. It is found…
We discuss various properties of the variational class of continuous matrix product states, a class of ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful…
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and…
We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly-solvable Calogero-Moser model. We show the high…
Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on…
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…
We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory…
A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the…
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with…
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with…
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…
We show how continuous matrix product states of quantum field theories can be described in terms of the dissipative non-equilibrium dynamics of a lower-dimensional auxiliary boundary field theory. We demonstrate that the spatial correlation…