We present the zero-temperature phase diagram of a square lattice quantum spin-1/2
XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the
XY order, striped or valence bond solid, staggered N\'eel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.
We study ring-exchange models for bosons or
XY spins on a triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbor exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin (superfluid) stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.
We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.
We describe a stochastic series expansion quantum Monte Carlo method for a two-dimensional S = 1/2 XY model (or, equivalently, hard-core bosons at half filling) which in addition to the standard pair interaction J includes a four-site term K that flips spins on a square plaquette. The model has three ordered ground state phases; for K/J approximately < or = 8 it has long-range xy spin order (superfluid bosons), for K/J approximately > or = 15 it has staggered spin order in the z direction (charge-density wave), and between these phases it is in a state with columnar order in the bond and plaquette energy densities. We discuss an implementation of directed-loop updates for the SSE simulations of this model and also introduce a "multibranch" cluster update which significantly reduces the autocorrelation times for large K/J. In addition to the pure J-K model, which in the z basis has only off-diagonal terms, we also discuss modifications of the algorithm needed when various diagonal interactions are included.
The nature of quantum spin liquids is studied for the spin-
1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites,
J1, and those between next-nearest-neighbor sites,
J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region
0.4<J2/J1≤0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of
0.4<J2/J1≤0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for
0.5<J2/J1≤0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the
C4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation
⟨S(0)S(r)⟩∝1/rz+η at a long distance
r appears to increase from
z+η∼1 at
J2/J1∼0.4 toward the continuous transition to the VBC phase at
J1/J1∼0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.
We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the
s=1/2 next-next-nearest-neighbor Heisenberg antiferromagnet on the square lattice, with additional four-spin ring exchange from higher-order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters
t/U to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling
Jr, which have been varied between
0J and 1.
5J. We find that ring exchange induces a quantum phase transition from a $(\ensuremath{\pi},\ensuremath{\pi})$ ordered state to a $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ ordered state. This quantum critical point is reduced by quantum fluctuations from its mean-field value of
Jr/J=2 to a value of $\ensuremath{\sim}1.1$. At the quantum critical point, the dynamical correlation function shows a pseudocontinuum at
q values between the two competing ordering vectors.