13 research outputs found
An Efficient Density Matrix Renormalization Group Algorithm for Chains with Periodic Boundary Condition
The Density Matrix Renormalization Group (DMRG) is a state-of-the-art
numerical technique for a one dimensional quantum many-body system; but
calculating accurate results for a system with Periodic Boundary Condition
(PBC) from the conventional DMRG has been a challenging job from the inception
of DMRG. The recent development of the Matrix Product State (MPS) algorithm
gives a new approach to find accurate results for the one dimensional PBC
system. The most efficient implementation of the MPS algorithm can scale as
O(), where can vary from 4 to . In this paper, we
propose a new DMRG algorithm, which is very similar to the conventional DMRG
and gives comparable accuracy to that of MPS. The computation effort of the new
algorithm goes as O() and the conventional DMRG code can be easily
modified for the new algorithm.Comment: 7 pages, 4 figure
Quantum phase transition in skewed ladders: an entanglement entropy and fidelity study
Entanglement entropy (EE) of a state is a measure of correlation or
entanglement between two parts of a composite system and it may show
appreciable change when the ground state (GS) undergoes a qualitative change in
a quantum phase transition (QPT). Therefore, the EE has been extensively used
to characterise the QPT in various correlated Hamiltonians. Similarly fidelity
also shows sharp changes at a QPT. We characterized the QPT of frustrated
antiferromagnetic Heisenberg spin-1/2 systems on 3/4, 3/5 and 5/7 skewed
ladders using the EE and fidelity analysis. It is noted that all the
non-magnetic to magnetic QPT boundary in these systems can be accurately
determined using the EE and fidelity, and the EE exhibits a discontinuous
change, whereas fidelity shows a sharp dip at the transition points. It is also
noted that in case of the degenerate GS, the unsymmetrized calculations show
wild fluctuations in the EE and fidelity even without actual phase transition,
however, this problem is resolved by calculating the EE and the fidelity in the
lowest energy state of the symmetry subspaces, to which the degenerate states
belong.Comment: 9 pages, 10 figure
Study of Interacting Heisenberg Antiferromagnet Spin-1/2 and 1 Chains
Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits