The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange J2 > 0 between first neighbors in the legs, variable isotropic AF exchange J1 between some first neighbors in different legs, and an unpaired spin per odd-membered ring when J1 J2. Ladders with skewed rungs and variable J1 have frustrated AF interactions leading to multiple quantum phases: AF at small J1, either F or AF at large J1, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate J1.
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(p × m 3 ), where p can vary from 4 to m 2 . 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(m 3 ) and the conventional DMRG code can be easily modified for the new algorithm.
Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings J 1 . These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with J 2 1 , and the systems show an incommensurate phase for 0.0 < J 1 < 1.0. The spin-spin correlation functions in the incommensurate phase follow power law decay which is very similar to Heisenberg antiferromagnetic chain in external magnetic field. In large J 1 limit, the normal ladder behaves like a collection of singlet dimers, whereas the zigzag ladder behaves as a one dimensional spin-1/2 antiferromagnetic chain. Figure 1: (a) and (b) show the normal and the zigzag arrangements of the interfaces. The arrows show the spin arrangement and the question mark represents the frustrated spin.12]. Ladders with ferromagnetic legs/rungs and antiferromagnetic rungs/legs are also well studied and show interesting phases [14][15][16][17][18][19]. However, the AF zigzag ladder is completely different from normal ladder. The zigzag ladder in the weak rung coupling limit J 1 /J 2 < 0.44 behaves like two independent HAF spin-1/2 chains [2,20,21], and shows gapped spiral phase for 0.44 < J 1 < 2. It is gapped system with dimer configuration for 2 < J 1 /J 2 < 4.148 [2,[20][21][22][23].In this paper we consider spin ladders which have ferromagnetic (F) spin exchange interactions along one of the legs, and antiferromagnetic (AF) interactions on the other leg; and spins on these two legs are interacting through AF interaction. The focus of this paper is to study some universal theoretical aspects such as the existence of exotic phases in the ground state (GS) and low-lying excitations in this system. We show that the ferromagnetic-antiferromagnetic (F-AF) ladders pose quasi-long range behavior in incommensurate regime, and frustration can be induced even for very small rung coupling limit.These two lagged ladders can represent the interface of the two layered magnetic spin-1/2 system consisting of an antiferromagnetic and a ferromagnetic layer where the two layers interact with direct or indirect antiferromagnetic exchange. Similar interfaces are studied by Suhl et al. [24] and Hong et al. [25]. We further simplify the model by considering only a inter-facial line of spins in the interface of both the layers. We consider two possibilities of arrangement of inter-facial spins; first, when spins are directly facing each-other as in normal ladder (NL), and second, where spins on one leg is shifted by half of the lattice unit forming a zigzag ladder (ZL). The spin arrangements of NL and ZL are shown in the Fig. 1(a) and (b). These systems are interesting because both the ladders are frustrated irrespective to the nature of rung in...
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