Phase Diagram of Spin Ladder Models and the Topology of Short Range Valence Bonds

Masaaki Nakamura

Eugene H. Kim, Gábor Fáth, Jenő Sólyom +1 more

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide into two topologically distinct classes, and as a consequence, there exist two topologically distinct types of string order. Therefore, not all gapped phases belong to the same universality class. We show that phase transitions occur when we interpolate between models belonging to different topological classes, and we study the nature of these transitions.

Gábor Fáth, Örs Legeza, Jenő Sólyom

Two-leg spin ladders have a rich phase diagram if rung, diagonal, and plaquette couplings are allowed for. Among the possible phases there are two Haldane-type spin liquid phases without local order parameter, which differ, however, in the topology of the short range valence bonds. We show that these phases can be distinguished numerically by two different string order parameters. We also point out that long-range string and dimer orders can coexist.

Smitha Vishveshwara, Wade DeGottardi, Diptiman Sen

Wen-Yuan Liu, Didier Poilblanc, Shou-Shu Gong +2 more

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-$\frac{1}{2}$ square-lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ antiferromagnetic (AFM) Heisenberg model. The ground-state phase diagram is established with a rich variety of phases: the N\'eel AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe AFM, and incommensurate spiral phases. The nature of the VBS region is revealed, which contains a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlation in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exist several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ antiferromagnet at zero temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum spin systems that may host nonuniform features by means of the finite PEPS.

Oleg A. Starykh, Takashi Hikihara