Related papers: Matrix Product States, Projected Entangled Pair St…
Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
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…
The density matrix renormalization group (DMRG) approach is arguably the most successful method to numerically find ground states of quantum spin chains. It amounts to iteratively locally optimizing matrix-product states, aiming at better…
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, needed to transmit entanglement over arbitrary…
Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state…
Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped, topologically ordered systems. The defining feature of these representations is that…
Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this…
We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the…
We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of non-deterministic quantum…
The quantum renormalization group method is applied to study the quantum criticality and entanglement entropy of the ground state of the Ising chain in the presence of antisymmetric anisotropic couplings and alternating exchange…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for capturing ground state physics of two-dimensional quantum systems. However, accurately computing and minimizing the energy expectation value remains…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
The task of changing the overlap between two quantum states can not be performed by making use of a unitary evolution only. However, by means of a unitary-reduction process it can be probabilistically modified. Here we study in detail the…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…