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Register a new userQuantum phases of a frustrated spin-1 system: the 5/7 skewed ladder
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The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings is studied numerically using exact diagonalization technique up to 16 spins and using density matrix renormalization group method for larger system sizes. The ladder has isotropic antiferromagnetic (AF) exchange interaction ($J_2 = 1$) between the nearest neighbor spins along the legs, varying isotropic AF exchange interaction ($J_1$) along the rungs. As a function of $J_1$, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic gs to different kinds of ferrimagnetic gs. Study of different gs properties such as spin gap, spin-spin correlations, spin density and bond order reveal that the system has four distinct phases namely, AF phase at small $J_1$, ferrimagnetic phase with gs spin $S_G = n$ for $1.44 < J_1 < 4.74$ and with $S_G = 2n$ for $J_1 > 5.63$, where $n$ is the number of unit cells, a reentrant nonmagnetic phase at $4.74 < J_1 < 5.44$. The system also shows the presence of spin current at specific $J_1$ values due to simultaneous breaking of both reflection and spin parity symmetries.
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Magnetization plateaus are some of the most striking manifestations of frustration in low-dimensional spin systems. We present numerical studies of magnetization plateaus in the fascinating spin-1/2 skewed ladder system obtained by alternately fusing five- and seven-membered rings. This system exhibits three significant plateaus at $m = 1/4$, $1/2$ and $3/4$, consistent with the Oshikawa-Yamanaka-Affleck condition. Our numerical as well as perturbative analysis shows that the ground state can be approximated by three weakly coupled singlet dimers and two free spins, in the absence of a magnetic field. With increasing applied magnetic field, the dimers progressively become triplets with large energy gaps to excited states, giving rise to stable magnetization plateaus. Finite-temperature studies show that $m=1/4$ and $1/2$ plateaus are robust and survive thermal fluctuations while the $m=3/4$ plateau shrinks rapidly due to thermal noise. The cusps at the ends of a plateau follow the algebraic square-root dependence on $B$.
We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for $J_1 ge 1.82$; the gs spin corresponds to ferromagnetic alignment of effective $S = 2$ objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning $J_1$ in a finite size system. The switching pattern is nonmonotonic as a function of $J_1$, and depends on the system size. It appears to be the consequence of higher $J_1$ favoring higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin parity and mirror symmetry breaking giving rise to spin current in the gs of the system.
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 $J_1$.
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.
We report experimental and theoretical evidence that Rb$_2$Cu$_2$Mo$_3$O$_{12}$ has a nonmagnetic tetramer ground state of a two-leg ladder comprising antiferromagnetically coupled frustrated spin-$1/2$ chains and exhibits a Haldane spin gap of emergent spin-1 pairs. Three spin excitations split from the spin-1 triplet by a Dzyaloshinskii-Moriya interaction are identified in inelastic neutron-scattering and electron spin resonance spectra. A tiny magnetic field generates ferroelectricity without closing the spin gap, indicating a novel class of ferroelectricity induced by a vector spin chirality order.
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