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تسجيل مستخدم جديدSpin structure factor and quantum phases of frustrated spin-1/2 chains
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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.
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ween 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 $alpha_1(Delta)$.
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