We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each step, has been used to reach the target system size. We then need to obtain the ground state for a different system size for every site addition, so 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D system consists of an array of nonequivalent sites as in ladders or Hubbard-Holstein model, special care has to be taken. Our procedure, which we call the {\it recursive sweep method}, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model as well as more complicated ones such as the Hubbard-Holstein model.We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each step, has been used to reach the target system size. We then need to obtain the ground state for a different system size for every site addition, so 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D system consists of an array of nonequivalent sites as in ladders or Hubbard-Holstein model, special care has to be taken. Our procedure, which we call the {\it recursive sweep method}, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model as well as more complicated ones such as the Hubbard-Holstein model.

arXiv:cond-mat/0702242Journal of the Physical Society of JapanApr 25, 20072 citations

XXZ spin- 12 representation of a finite- U Bose-Hubbard chain at half-integer filling

Domenico Giuliano, Davide Rossini, Pasquale Sodano +1 more

Using a similarity Hamiltonian renormalization procedure, we determine an effective spin- $\frac{1}{2}$ representation of the Bose-Hubbard model at half-integer filling and at a finite onsite interaction energy $U$ . By means of bosonization, we are able to recast the effective Hamiltonian as that of a spin- $\frac{1}{2}$ XXZ magnetic chain with pertinently renormalized coupling and anisotropy parameters. We use this mapping to provide analytical estimates of the correlation functions of the Bose-Hubbard model. We then compare such results with those based on density matrix renormalization group numerical simulations of the Bose-Hubbard model for various values of $U$ and for a number $L$ of lattice sites as low as $L\ensuremath{\sim}30$. We find an excellent agreement up to $10%$ between the output of analytical and numerical computations, even for relatively small values of $U$ . Our analysis implies that, also at finite $U$ , the one-dimensional Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-$\frac{1}{2}$ representation of the Bose-Hubbard model at half-integer filling and at a finite onsite interaction energy $U$. By means of bosonization, we are able to recast the effective Hamiltonian as that of a spin-$\frac{1}{2}$ XXZ magnetic chain with pertinently renormalized coupling and anisotropy parameters. We use this mapping to provide analytical estimates of the correlation functions of the Bose-Hubbard model. We then compare such results with those based on density matrix renormalization group numerical simulations of the Bose-Hubbard model for various values of $U$ and for a number $L$ of lattice sites as low as $L\ensuremath{\sim}30$. We find an excellent agreement up to $10%$ between the output of analytical and numerical computations, even for relatively small values of $U$. Our analysis implies that, also at finite $U$, the one-dimensional Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.

arXiv:1210.2685Physical Review BJan 3, 201321 citations

Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-

\frac{1}{2}

representation of the Bose-Hubbard model at half-integer filling and at a finite onsite interaction energy

U

. By means of bosonization, we are able to recast the effective Hamiltonian as that of a spin-

\frac{1}{2}

XXZ magnetic chain with pertinently renormalized coupling and anisotropy parameters. We use this mapping to provide analytical estimates of the correlation functions of the Bose-Hubbard model. We then compare such results with those based on density matrix renormalization group numerical simulations of the Bose-Hubbard model for various values of

U

and for a number

L

of lattice sites as low as $L\ensuremath{\sim}30$. We find an excellent agreement up to

10%

between the output of analytical and numerical computations, even for relatively small values of

U

. Our analysis implies that, also at finite

U

, the one-dimensional Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.