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...

Recurrent apthous stomatitis (RAS) is one of the most common oral inflammatory diseases characterised by painful recurrent ulcerations of the orofacial region. The ulcers occur in three clinical forms: minor, major and herpetiform. Several therapies have been advocated to manage these lesions such as topical corticosteroids (triamcinolone acetonide, hydrocortisone acetate and clobetasol propionate), chlorhexidine mouth rinses, tetracycline oral rinses, thalidomide, fluocinonide, colchicines and the immune boosting agent levamosile, vitamin therapy and topical interferon α-2a. Laser therapy is used as an alternative method in treatment of RAS. In this paper one patient with RAS was treated using a 940 nm diode laser for symptomatic relief of pain and burning sensation and healing of ulcer.

The ground state properties of a frustrated spin-1/2 system is studied on a trellis ladder which is composed of two zigzag ladders interacting through rung interactions. The presence of rung interaction between the zigzag ladders induces a non-magnetic ground state, although, each of zigzag ladders has ferromagnetic order in weak anti-ferromagnetic leg interaction limit. The rung interaction also generates rung dimers and opens spin gap which increases rapidly with rung interaction strength. The correlation between spins decreases exponentially with the distance between them. Figure 1: Two coupled zigzag ladders form trellis ladder. The broken lines show the extension of trellis ladder to trellis lattice structure. The arrows show respective spin arrangements. The reference site is labeled by '0' and the distances of all other sites are shown with respect to it. The distance of the sites in the same zigzag ladder as the reference site are written in bold numbers, and the sites on the other ladder are written in normal numbers.and rung couplings of a normal ladder, respectively and J 1 is inter-ladder coupling through zigzag bonds.There are several theoretical studies for two coupled zigzag ladders, e.g. a two-leg honeycomb ladder is considered in Ref. [19], where both J 1 and J 2 are AFM, but J 3 can be either FM or AFM. This system shows two types of Haldane phases for the FM J 3 and, columnar dimer and rung singlet phases for the AFM J 3 . Normand et al. considered the similar coupled ladders with all three AFM J 1 , J 2 and J 3 interactions. They find dimerized chains for large J 2 and small J 3 limit, spiral long range order for both large J 2 and J 3 limit, Néel long range order in the small J 2 < 0.4 and for all J 3 [20]. Ronald et al. have shown the effect of inter-chain coupling on spiral ground state of J 1 − J 2 model [21]. The effect of inter-ladder coupling on spin gap and magnon dispersion has been discussed in [22] exploiting a theoretical model which has also been

We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two J1 − J2 zigzag ladders interacting through anti-ferromagnetic rung couplings J3. The J1 and J2 are ferromagnetic zigzag spin interaction between two legs and anti-ferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group (DMRG) method and linearized spin wave analysis. In small J2 limit a short range stripe collinear phase is found in the presence of J3, whereas, in the large J2/J3 limit non-collinear quasi-long range phase is found. The system shows a short range non-collinear state in large J3 limit. The short range order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin wave analysis show similar phase boundary between stripe collinear and non-collinear short range phases, and the collinear phase region shrinks with increasing J3. We apply this model to understand the magnetic properties of CaV2O5 and also fit the experimental data of susceptibility and magnetization. The variation of magnetic specific heat capacity as function of external magnetic field is also predicted. We note that J3 is a dominant interaction in this system, whereas J1 and J2 are approximately half of J3.