2015/07/14 by Manoranjan Kumar, Kumar, Manoranjan, Aslam Parvej +3 · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Strong Light-Matter Interactions
paper · pdf · doi:10.48550/arxiv.1507.03720
The spin-1/2 chain with isotropic Heisenberg exchange J1, J2 > 0\nbetween first and second neighbors is frustrated for either sign of J1. Its\nquantum phase diagram has critical points at fixed J1/J2 between gapless\nphases with nondegenerate ground state (GS) and quasi-long-range order (QLRO)\nand gapped phases with doubly degenerate GS and spin correlation functions of\nfinite range. In finite chains, exact diagonalization (ED) estimates critical\npoints as level crossing of excited states. GS spin correlations enter in the\nspin structure factor S(q) that diverges at wave vector qm in QLRO(qm)\nphases with periodicity 2\π/qm but remains finite in gapped phases.\nS(qm) is evaluated using ED and density matrix renormalization group (DMRG)\ncalculations. Level crossing and the magnitude of S(qm) are independent and\ncomplementary probes of quantum phases, based respectively on excited and\nground states. Both indicate a gapless QLRO(\π/2) phase between -1.2 <\nJ1/|J2| < 0.45. Numerical results and field theory agree well for quantum\ncritical points at small frustration J2 but disagree in the sector of weak\nexchange J1 between Heisenberg antiferromagnetic chains on sublattices of\nodd and even-numbered sites.\n