Related papers: Entanglement renormalization
We study the ground state entanglement entropy of the quantum Dyson hierarchical spin chain in which the interaction decays algebraically with the distance as $r^{-1-\sigma}$. We exploit the real-space renormalisation group solution which…
We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum…
A generic scheme is proposed to investigate the entanglement entropy for a type of scale-invariant states, valid for orthonormal basis states in the ground state subspace of quantum many-body systems undergoing spontaneous symmetry breaking…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
We consider quantum states under the renormalization-group (RG) transformations introduced by Verstraete et al. [Phys. Rev. Lett. 94, 140601 (2005)] and propose a quantification of entanglement under such RG (via the geometric measure of…
Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to…
Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we…
A universal finite system-size scaling analysis of the entanglement entropy is presented for highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes in exactly solvable one-dimensional quantum…
We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This…
A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size…
We present an elementary introduction to entanglement renormalization, a real space renormalization group for quantum lattice systems. This manuscript corresponds to a chapter of the book "Understanding Quantum Phase Transitions", edited by…
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 qubits. With the technique of holographic quantum…
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than non-critical states. Standard algorithms for one-dimensional many-particle systems construct model…
We present simulations of causal dynamical collapse models of field theories on a 1+1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the…
Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size.…
We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal…