Manoranjan Kumar

Tuning the bond-order wave phase in the half-filled extended Hubbard model

Theoretical and computational studies of the quantum phase diagram of the one-dimensional half-filled extended Hubbard model (EHM) indicate a narrow bond-order wave (BOW) phase with finite magnetic gap E-m for on-site repulsion U < U-*, the critical point, and nearest-neighbor interaction V-c approximate to U/2 near the boundary of the charge-density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher U-* and wider BOW phase. Density-matrix renormalization group is used to obtain E-m directly as the singlet-triplet gap, with finite E-m marking the BOW boundary V-s(U). The BOW/CDW boundary V-c(U) is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of U-* based on a metallic point at V-c(U) for U < U-*. Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients.

Dimerization transition of alkali-TCNQ salts: Charge degrees of freedom near the CDW boundary

Stacks of TCNQ − radical ions in 1 : 1 alkali salts are shown to be near the chargedensity- wave (CDW) boundary, where charge degrees of freedom induce strong dimerization δ.Charge-transfer absorption and δ(V ) are obtained for a one-dimensional (1D) Hubbard model with long-range Coulomb interactions V that ranges from spin-Peierls at V =0 to the CDW boundary at Vc and beyond. Cation dimerization lifts the degeneracy of Peierls systems and confers 3D contributions to the dimerization transition of alkali-TCNQ salts.

Scaling exponents in spin-

In conformal field theory, key properties of spin-1/2 chains, such as the ground state energy per site and the excitation gap scale with dimerization δ as δ with known exponents α and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next nearest neighbor interactions (J2), for J2c=0.2411. DMRG analysis of a frustrated spin chain with no logarithmic corrections yields the field theoretic values of α, and scaling relation is valid up to the physically realized range, δ ~ 0.1. However, chains with logarithmic corrections (J2<0.2411J) are more accurately fit by simple power laws with different exponents for physically realized dimerizations. We show the exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from approximately 3/2 to 4/3 for the energy per site and error bars in the exponent also decrease as J2 approaches to J2c. PACs number: 75.10.Pq, 75.10.Jm The linear Heisenberg antiferromagnet (HAF) of spin-1/2 sites is an important and unique model many-body system that is both experimentally realized (in organic and inorganic crystals) and is theoretically amenable to exact solution. As discussed in Refs.2 and 3, bozonization and conformal field theories have motivated recent theoretical interest in HAFs and dimerized spin chains and provide scaling laws for stabilization of the ground state energy per site as well as the magnitude of spin gap, as a function of the dimerization δ. However, the spin gap at experimentally realized dimerization, does not follow scaling. Scaling theory leaves open the range of dimerization over which scaling results are reliable, while experiment requires HAFs with substantial dimerization that may be outside the range of scaling. Frustration in AF systems is another broad topic of current interest. For example, a frustrated HAF has a second-neighbor exchange J2 that yields a valence-bond solid at J2 = 1/2. Since the scaling of the dimerization gap depends on J2, an HAF with both dimerization and frustration 6 is well suited to study scaling exponents, logarithmic corrections and the dimerization range of scaling. The Hamiltonian with nearest-neighbor exchange J = 1, taken as the unit of energy, is 2 ( , ) [1 ( 1) ] n n n n n n H J s s J s s δ δ 1 2 2 + + = + − ⋅ + ⋅ ∑ (1) The parameters δ and J2 > 0 describe dimerization and frustration, respectively. The regular HAF with δ = J2 = 0 in Eq. (1) has ground state (GS) energy per site of ε0= –ln2 +1/4 and vanishing singlet-triplet (ST) gap ∆(0,0) = 0. The ST gap, ∆(0,J2), opens at J2c = 0.2411, that marks the transition from magnetic to nonmagnetic ground state . In this brief report, we use the density matrix renormalization group (DMRG) method to find the ST gap and GS energy per site of the infinite chain. We analyze the results for δ << 1 and J2 ≤ J2c as

^{(1/2)}

The spin-1/2 chain with isotropic exchange J1, J2 > 0 between first and second neighbors is frustrated for either sign of J1 and has a singlet ground state (GS) for J1/J2 ⩾ -4. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J1/J2 are evaluated using exact diagonalization and density matrix renormalization group calculations. The wave vector qG of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor S(q). Variable qG indicates IC phases in two J1/J2 intervals, [-4, - 1.24] and [0.44, 2], and a C-IC point at J1/J2 = 2. The decoupled C phase in [-1.24, 0.44] has constant qG = π/2, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, E m and Eσ, are degenerate in finite systems at specific frustration J1/J2. Level crossing extrapolates in the thermodynamic limit to the same critical points as qG. The S(q) peak diverges at qG = π in the gapless phase with J1/J2 > 4.148 and quasi-long-range order (QLRO(π)). S(q) diverges at ±π/2 in the decoupled phase with QLRO(π/2), but is finite in gapped phases with finite-range correlations. Numerical results and field theory agree at small J2/J1 but disagree for the decoupled phase with weak exchange J1 between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO(π/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

Heisenberg chains with dimerization and frustration studied with the density-matrix renormalization group

The spin-1/2 chain with isotropic Heisenberg exchange J1, J2  >  0 between first and second neighbors is frustrated for either sign of J1. Its quantum phase diagram has critical points at fixed J1/J2 between gapless phases with nondegenerate ground state (GS) and quasi-long-range order (QLRO) and gapped phases with doubly degenerate GS and spin correlation functions of finite range. In finite chains, exact diagonalization (ED) estimates critical points as level crossing of excited states. GS spin correlations enter in the spin structure factor S(q) that diverges at wave vector qm in QLRO(q(m)) phases with periodicity 2π/q(m) but remains finite in gapped phases. S(q(m)) is evaluated using ED and density matrix renormalization group (DMRG) calculations. Level crossing and the magnitude of S(q(m)) are independent and complementary probes of quantum phases, based respectively on excited and ground states. Both indicate a gapless QLRO(π/2) phase between  -1.2  <  J1/|J2|  <  0.45. Numerical results and field theory agree well for quantum critical points at small frustration J2 but disagree in the sector of weak exchange J1 between Heisenberg antiferromagnetic chains on sublattices of odd and even-numbered sites.

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J 1, J 2 between first and second neighbors

The quantum phases of one-dimensional spin

Level crossing, spin structure factor and quantum phases of the frustrated spin-1/2 chain with first and second neighbor exchange

s=1/2

Decoupled phase of frustrated spin- 1 2 antiferromagnetic chains with and without long-range order in the ground state

chains are discussed for models with two parameters, frustrating exchange

Density matrix renormalization group algorithm for Bethe lattices of spin-1/2 or spin-1 sites with Heisenberg antiferromagnetic exchange

g={J}_{2}g0