Related papers: Tensor networks and the numerical renormalization …
In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…
We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on the renormalization group (RG) theory for PDEs, appeared…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
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…
Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…
We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
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…
Accurate numerical simulations of a doped t-J model on a two-leg ladder are presented for the particle number, chemical potential, magnetic susceptibility and entropy in the limit of large exchange coupling on the rung using a finite…
We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum…
In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…
We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…