Related papers: Tensor network renormalization yields the multi-sc…
We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z_2 x Z_2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum…
We propose a second renormalization group method to handle the tensor-network states or models. This method reduces dramatically the truncation error of the tensor renormalization group. It allows physical quantities of classical…
We describe a numerical many-body technique that is based on both tensor networks and quantum Monte Carlo. The variational ansatz is a tensor network that can harvest volume-law entanglement. It is constructed from a tensor train to which…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space---the geometry of CFT intervals. In holographic theories kinematic space becomes…
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In…
The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the…
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that…
The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD),…
In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the…
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary onsite symmetries can be gauged within…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\hat\rho=e^{-\beta \hat{H}}$ onto itself. We refer to…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to…