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The static structure factor S(q) of frustrated spin-1/2 chains with isotropic exchange and a singlet ground state (GS) diverges at wave vector q_m when the GS has quasi-long-range order (QLRO) with periodicity 2pi/q_m but S(q_m) is finite in bond-order-wave (BOW) phases with finite-range spin correlations. Exact diagonalization and density matrix renormalization group (DMRG) calculations of S(q) indicate a decoupled phase with QLRO and q_m = pi/2 in chains with large antiferromagnetic exchange between second neighbors. S(q_m) identifies quantum phase transitions based on GS spin correlations.
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The spin-1/2 chain with isotropic Heisenberg exchange $J_1$, $J_2 > 0$ between first and second neighbors is frustrated for either sign of J1. Its quantum phase diagram has critical points at fixed $J_1/J_2$ 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 $q_m$ in QLRO($q_m$) phases with periodicity $2pi/q_m$ 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($pi/2$) phase between $-1.2 < J_1/|J_2| < 0.45$. Numerical results and field theory agree well for quantum critical points at small frustration $J_2$ but disagree in the sector of weak exchange $J_1$ between Heisenberg antiferromagnetic chains on sublattices of odd and even-numbered sites.
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 $J_2 > 0$ between first neighbors in the legs, variable isotropic AF exchange $J_1$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when $J_1 gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F or AF at large $J_1$, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate $J_1$.
Exact diagonalization of finite spin-1/2 chains with periodic boundary conditions is applied to the ground state (gs) of chains with ferromagnetic (F) exchange $J_1 < 0$between first neighbors, antiferromagnetic (AF) exchange $J_2 = alpha J_1 > 0$between second neighbors, and axial anisotropy $0 le Delta le 1$. In zero field, the gs is in the $S_z = 0$ sector for the relevant parameters and is doubly degenerate at multiple points $gamma_m = (alpha_m, Delta_m)$ in the $alpha$, $Delta$ plane. Degeneracy under inversion at sites or spin parity or both leads, respectively, to a bond order wave (BOW), to staggered magnetization or to vector chiral (VC) order. Exact results up to $N = 28$ spins directly yield order parameters and spin correlation functions whose weak N dependencies allow inferences about infinite chains. The high-spin gs at $J_2 = 0$ changes discontinuously at $gamma_1 = (-1/4, 1)$ to a singlet in the isotropic ($Delta = 1$) chain. The transition from high to low spin $S(alpha, Delta)$ is continuous for $ Delta < Delta_B = 0.95 pm 0.01$ on the degeneracy line $alpha_1(Delta)$. The gs has staggered magnetization between $Delta_A = 0.72$ and $Delta_B$, and a BOW for $Delta < Delta_A$. When both inversion and spin parity are reversed at $gamma_m$, the correlation functions $C(p)$ for spins separated by $p$ sites are identical. $C(p)$ minima are shifted by $pi/2$ from the minima of VC order parameters at separation $p$, consistent with right and left-handed helices along the z axis and spins in the xy plane. Degenerate gs of finite chains are related to quantum phase diagrams of extended $alpha$, $Delta$ chains, with good agreement for order parameters along the line $alpha_1(Delta)$.
We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1-frac2N$ ($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a fraction $frac1N$ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the M=0 plateau. Concentrating on the $frac13$ plateau (N=3) we unravel the microscopic structure of the domain walls which carry fractional spin-$frac13$, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.
We study a spin-5/2 antiferromagnetic trimerized chain substance SrMn3P4O14 using neutron powder diffraction experiments. The coplanar spiral magnetic structure appears below T_N1 = 2.2(1) K. Values of several magnetic structure parameters change rapidly at T_N2 = 1.75(5) K, indicating another phase transition, although the magnetic structures above and below T_N2 are the qualitatively same. The spiral magnetic structure can be explained by frustration between nearest-neighbor and next-nearest-neighbor exchange interactions in the trimerized chains.
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