Non-hermitian problems and some other aspects

Peschel, Ingo; Kaulke, M.

doi:10.1007/bfb0106078

Cited by 47 publications

(65 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to access the transition scenario in the long chain-length limit, we have studied chains up to L=512 using the DMRG method [28][29][30]. The fact that the transition at U c is connected to a change in inversion symmetry requires some caution when open boundary conditions (OBC) are used in DMRG studies.…”

Section: A Excitation Gapsmentioning

confidence: 99%

Nature of the insulating phases in the half-filled ionic Hubbard model

Kampf

Sekania

Japaridze

et al. 2003

J. Phys.: Condens. Matter

122

View full text Add to dashboard Cite

We investigate the ground-state phase diagram of the one-dimensional "ionic" Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group (DMRG) methods. We identify an insulatorinsulator phase transition from a band to a correlated insulator with simultaneous charge and bondcharge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.

show abstract

Section: A Excitation Gapsmentioning

confidence: 99%

Nature of the insulating phases in the half-filled ionic Hubbard model

Kampf

Sekania

Japaridze

et al. 2003

J. Phys.: Condens. Matter

122

View full text Add to dashboard Cite

show abstract

“…From the viewpoint of block entropies a spin-chain version of the Kondo model has been studied 14,15 using density matrix renormalization group (DMRG) methods 16,17 . Here a different geometry was considered with an impurity spin coupled to one end of a finite chain.…”

Section: Introductionmentioning

confidence: 99%

Fano resonances and entanglement entropy

Eisler

Garmon

2010

Phys. Rev. B

View full text Add to dashboard Cite

We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.

show abstract

“…In the stochastic TMRG (for a description of the very similar TMRG applied to quantum systems, see [2]), one considers a stochastically evolving system extended infinitely in one spatial dimension with (for simplicity) local update rules involving neighbouring sites only that allow a finite number of states (n). The local interaction between two (or similarly, a few) lattice sites is given by the local transfer matrix (τ )…”

Section: The Tmrg Transfer Matrixmentioning

confidence: 99%

“…Since its inception in 1992 by White [1], the Density Matrix Renormalization Group (DMRG) has emerged as one of the most powerful numerical methods in the study of low dimensional strongly correlated fermionic, bosonic or quantum magnetic systems [2]. The universality of its core idea of deducing a decimation prescription for state spaces by considering the renormalization flow of suitable reduced density matrices has led many researchers to extend the method to other fields of research in systems with many correlated degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

On the choice of the density matrix in the stochastic TMRG

Enss¹,

Schollwoeck²

2001

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Abstract. In applications of the density matrix renormalization group to nonhermitean problems, the choice of the density matrix is not uniquely prescribed by the algorithm. We demonstrate that for the recently introduced stochastic transfer matrix DMRG (stochastic TMRG) the necessity to use open boundary conditions makes asymmetrical reduced density matrices, as used for renormalization in quantum TMRG, an inappropriate choice. An explicit construction of the largest left and right eigenvectors of the full transfer matrix allows us to show why symmetrical density matrices are the correct physical choice.

show abstract

Non-hermitian problems and some other aspects

Cited by 47 publications

References 14 publications

Nature of the insulating phases in the half-filled ionic Hubbard model

Nature of the insulating phases in the half-filled ionic Hubbard model

Fano resonances and entanglement entropy

On the choice of the density matrix in the stochastic TMRG

Contact Info

Product

Resources

About