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Register a new userAntiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
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We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.
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We consider the easy-plane limit of bipartite SU($N$) Heisenberg Hamiltonians which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary $N$, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$-colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $Nleq 5$ and valence-bond order for $N> 5$. By introducing SU($N$) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $Nleq 5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$, suggesting that easy-plane deconfined criticality runs away generically to a first order transition for small-$N$.
We calculate the bipartite von Neumann and second Renyi entanglement entropies of the ground states of spin-1/2 dimerized Heisenberg antiferromagnets on a square lattice. Two distinct dimerization patterns are considered: columnar and staggered. In both cases, we concentrate on the valence bond solid (VBS) phase and describe such a phase with the bond-operator representation. Within this formalism, the original spin Hamiltonian is mapped into an effective interacting boson model for the triplet excitations. We study the effective Hamiltonian at the harmonic approximation and determine the spectrum of the elementary triplet excitations. We then follow an analytical procedure, which is based on a modified spin-wave theory for finite systems and was originally employed to calculate the entanglement entropies of magnetic ordered phases, and calculate the entanglement entropies of the VBS ground states. In particular, we consider one-dimensional (line) subsystems within the square lattice, a choice that allows us to consider line subsystems with sizes up to $L = 1000$. We combine such a procedure with the results of the bond-operator formalism at the harmonic level and show that, for both dimerized Heisenberg models, the entanglement entropies of the corresponding VBS ground states obey an area law as expected for gapped phases. For both columnar-dimer and staggered-dimer models, we also show that the entanglement entropies increase but do not diverge as the dimerization decreases and the system approaches the Neel--VBS quantum phase transition. Finally, the entanglement spectra associated with the VBS ground states are presented.
We introduce a simple model of SO($N$) spins with two-site interactions which is amenable to quantum Monte-Carlo studies without a sign problem on non-bipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small $N$, a valence-bond solid (VBS) at large $N$ and a quantum spin liquid at intermediate $N$. By the introduction of a sign-free four-site interaction we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions.
We present the class of models of a nonmagnetic impurity in S=1/2 generalized ladder with an AKLT-type valence bond ground state, and of a S=1/2 impurity in the S=1 AKLT chain. The ground state in presence of impurity can be found exactly. Recently studied phenomenon of local enhancement of antiferromagnetic correlations around the impurity is absent for this family of models.
Every singlet state of a quantum spin 1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the singlet state, and are key ingredients in variational calculations. In this work, we study the bipartite valence bond distributions and their correlations within the ground state of the Heisenberg antiferromagnet on bipartite lattices. In terms of field theory, this problem can be mapped to correlation functions near a boundary. In dimension d >= 2, a non-linear sigma model analysis reveals that at long distances the probability distribution P(r) of valence bond lengths decays as |r|^(-d-1) and that valence bonds are uncorrelated. By a bosonization analysis, we also obtain P(r) proportional to |r|^(-d-1) in d=1 despite the different mechanism. On the other hand, we find that correlations between valence bonds are important even at large distances in d=1, in stark contrast to d >= 2. The analytical results are confirmed by high-precision quantum Monte Carlo simulations in d=1, 2, and 3. We develop a single-projection loop variant of the valence bond projection algorithm, which is well-designed to compute valence bond probabilities and for which we provide algorithmic details.
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