Theory of the kagome lattice Ising antiferromagnet in weak transverse fields (original) (raw)
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Physical Review B, 2005
General conditions in which disordered, spin liquid, and valence-bond ordered phases occur in quantum Ising antiferromagnets are studied using the prototype Kagome lattice spin models. A range of quantum dynamical processes in the Ising model, with and without total Ising spin conserved, are analytically shown to yield all three characteristic quantum paramagnetic phases in the Kagome system. Special emphasis is given to the XXZ model that can be sensibly compared to the Kagome lattice Heisenberg antiferromagnet. It is explicitly demonstrated that the total-spinconserving dynamics can yield a resonant valence bond (RVB) liquid phase with very short-ranged correlations, but also a valence-bond ordered phase compatible with the one proposed to explain the seemingly gapless singlet states of the Heisenberg antiferromagnet on the Kagome lattice. Likely consequences for generic spin models are discussed. The analysis combines compact U(1) gauge theory, duality transformations, lattice-field-theoretical methods, and variational approach.
Physics of low-energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
Physical Review B, 2003
This paper is concerned with physics of the low energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases-an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.
Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice
Physical review. B, Condensed matter, 1996
We have studied the compressible antiferromagnetic Ising Model on a triangular lattice using Monte Carlo simulations. It is found that the coupling to the strain removes the frustration of the rigid model and the simulations show a transition from the disordered to an ordered, striped phase at low temperatures. This transition involves two broken symmetries: the Ising symmetry and a three-state Potts symmetry characteristic of the triangular lattice. In the absence of bond fluctuations, this transition is always strongly first order. Using finite-size scaling analysis, we find evidence that, in the presence of fluctuations, the transition becomes weakly first order and possibly second order when the coupling to the lattice is increased. We discuss the relevance of this model to certain phase transitions in alloys.
Spin-Glass-Like Ordering in a Frustrated J1-J2 Ising Antiferromagnet on a Honeycomb Lattice
Acta Physica Polonica A, 2020
We study the nature of a low-temperature phase in the frustrated honeycomb-lattice Ising model with first-and second-neighbor antiferromagnetic (AF) interactions, J 1 and J 2 , respectively, for R = J 2 /J 1 > 1/4. It is known that for R < 1/4 there is a phase transition at low temperatures to the AF phase. Nevertheless, little is known about the critical behavior of the model for R > 1/4, except for recent effective field results which detected no phase transition down to zero temperature. Our Monte Carlo results suggest that for R > 1/4 there is at least one peculiar phase transition accompanied by a spin-glass-like freezing to a highly degenerate state consisting of frozen domains with stripe-type AF ordering separated by zero-energy domain walls. In spite of the local ordering within the respective domains there is no ordering among them and thus, unlike in the corresponding square-lattice model with R > 1/2, there is no conventional magnetic long-range ordering spanning the entire system.
2018
We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagome lattice by Monte Carlo simulations. A histogram data analysis shows that a second order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagome lattice excite the occurrence of a second order transition and unusual behavior of thermodynamic properties on the temperature dependence.
From classical to quantum Kagomé antiferromagnet in a magnetic field
Physical Review B, 2002
We study the magnetic properties of the Kagomé antiferromagnet going from the classical limit to the deep quantum regime of spin 1/2 systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for all S, in a wide range of XXZ anisotropies and for the occurrence of quantum order by disorder effects.
XXZ and Ising spins on the triangular kagome lattice
Physical Review B, 2008
The recently fabricated two-dimensional magnetic materials Cu9X2(cpa)6 • xH2O (cpa=2carboxypentonic acid; X=F,Cl,Br) have copper sites which form a triangular kagome lattice (TKL), formed by introducing small triangles ("a-trimers") inside of each kagome triangle ("b-trimer"). We show that in the limit where spins residing on b-trimers have Ising character, quantum fluctuations of XXZ spins residing on the a-trimers can be exactly accounted for in the absence of applied field. This is accomplished through a mapping to the kagome Ising model, for which exact analytic solutions exist. We derive the complete finite temperature phase diagram for this XXZ-Ising model, including the residual zero temperature entropies of the seven ground state phases. Whereas the disordered (spin liquid) ground state of the pure Ising TKL model has macroscopic residual entropy ln72 = 4.2767... per unit cell, the introduction of transverse (quantum) couplings between neighboring a-spins reduces this entropy to 2.5258... per unit cell. In the presence of applied magnetic field, we map the TKL XXZ-Ising model to the kagome Ising model with three-spin interactions, and derive the ground state phase diagram. A small (or even infinitesimal) field leads to a new phase that corresponds to a non-intersecting loop gas on the kagome lattice, with entropy 1.4053... per unit cell and a mean magnetization for the b-spins of 0.12(1) per site. In addition, we find that for moderate applied field, there is a critical spin liquid phase which maps to close-packed dimers on the honeycomb lattice, which survives even when the a-spins are in the Heisenberg limit.
The mother of all states of the kagome quantum antiferromagnet
One of the challenges in theoretical condensed matter physics is the physics of strongly correlated systems in regimes in which all interactions are nearly equally strong. This is particularly the case in quantum spin systems on geometrically frustrated lattices where, the inability to simultaneously satisfy competing exchange interactions, often results in the selection of magnetically ordered or exotic disordered spin liquid ground states. We report the existence of a quantum macroscopically degenerate ground state manifold in a simple model, the nearest neighbor antiferromagnetic XXZ model on the kagome lattice, for the ratio of Ising to antiferromagnetic transverse coupling Jz=−1/2. We explore the panoply of phases that emerge from this exactly solvable point and discuss its wider impact on the phase diagram of the kagome lattice antiferromagnet.
Partial lifting of degeneracy in the J1−J2−J3 Ising antiferromagnet on the kagome lattice
Physical Review B
Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical J1 − J2 − J3 Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for J1 > |J2|, |J3| based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate groundstate phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller J3 interactions, an indication of a very strong competition between low-energy states in this model.