相关论文: Renormalization group method for weakly coupled qu…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
Complex quantum systems are often multiscale in nature with strong interactions between different scales. We present a novel idea: iteratively suppressing, rather than tracing out, the fast, high-energy degrees of freedom in strongly…
A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained…
We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration examples, a…
A distributed-memory parallelization strategy for the density matrix renormalization group is proposed for cases where correlation functions are required. This new strategy has substantial improvements with respect to previous works. A…
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…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using low temperature perturbation theory. This type of transformations beyond $d=1$ is highly nontrivial even for free…
We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy…
For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can be also applied to two-dimensional planar lattices by regarding them as…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping…
The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The infinitesimal unitary transformation, introduced recently by F.Wegner, to bring the Hamiltonian to diagonal (or band diagonal) form, is applied to the Hamiltonian theory as an exact renormalization scheme. We consider QED on the light…
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of…
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a…