Phase Diagram of the 2D Fermionic Ring Exchange Only Model

Katharine Hyatt, Bryan Clark, Matthew P. A. Fisher

Mansoor A. S. Saqi, D S McKenzie

The 2D spin-1 ANNNI model is studied using an iterative method, the method of ring recurrence. The phase diagram is obtained numerically using matrices of order 9. The authors find the phase diagram to be generally similar to that of the 2D spin-1/2 ANNNI model.

Christian Borgs, Roman Kotecký

Vladimir Gritsev, Bruce Normand, D. Baeriswyl

We investigate the phase diagram of a generalized spin-1/2 quantum antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange interactions. We consider the exactly soluble models associated with the problem, obtain the exact ground states which exist for certain parameter regimes, and apply a variety of perturbative techniques in the regime of strong ring-exchange coupling. By combining these approaches with considerations related to the discrete ${Z}_{4}$ symmetry of the model, we present the complete phase diagram.

Norbert Kaiser

D. N. Sheng, Olexei I. Motrunich, Matthew P. A. Fisher

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., ``Bose surfaces.'' Signatures of this state, which we will refer to as a ``spin Bose metal'' (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular ``Bose points'' (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.