Quantum disordered ground state for hard-core bosons on the frustrated square lattice

Abstract

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-1/2 operators and the model can therefore be mapped onto an anisotropic J1-J2-Heisenberg model. We find the Néel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the x-y plane which result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or super-solids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing towards a quantum-disordered ground state for a small region in the phase diagram. PACS numbers: quantum spin frustration, 75.10.Jm; Magnetic phase transitions, 75.30.Kz; computer modeling and simulation 75.40.Mg

Anisotropic frustrated Heisenberg model on the honeycomb lattice

“…The phase diagram is very similar to the one found for the square lattice with nearest-and nextnearest-neighbor interactions, which was investigated for anisotropic exchange terms in Ref. 15. However, the stability region of the antiferromagnetic phases is reduced on the honeycomb lattice, which is explained by the lower coordination number of the lattice, thus the influence of quantum fluctuations is enhanced.…”

“…Furthermore, the direct transition line between the two antiferromagnetic states calculated via SE shows a steeper slope for the square lattice which also hints at a larger stability of this direct transition in that case. 15…”

Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model

“…This is the case, for example, in the J 1 − J 2 − J 3 kagome lattice XXZ model in the Ising limit 36 . Similar spin liquid phases have also been proposed for Ising limit XXZ models on the J 1 − J 2 square lattice and the J 1 − J 2 − J 3 honeycomb lattice 37,38 .…”

Phase diagrams of two-dimensional frustrated spin systems

“…outline and brief survey of main results chapter 2: interacting spin systems in two dimensions introduction of the investigated spin models, their main properties and a short outline of the applied framework of statistical mechanics chapter 3: computational methods exact diagonalization, (quantum) Monte-Carlo simulations and transfer matrix technique chapter 4: analytical methods series expansion and conformal field theory chapter 5: analysis of the phase transition for the Ising model on the frustrated square lattice [KHM11] evidence for first-order transition for a finite region of parameters (Monte-Carlo), perturbative derivation of the Ashkin-Teller field theory from the frustrated Ising model giving rise to non-universal critical behavior for the remaining parameters (conformal field theory) chapter 6: incommensurate ordering in a spatially anisotropic Ising model verification of an incommensurate phase between the paramagnetic and antiferromagnetic phase in the anisotropic Ising model, detection of several finite signals in the structure factor, a floating phase resembling a devil's staircase is identified (Monte-Carlo) chapter 7: quantum disordered ground state for hard-core bosons on the frustrated square lattice [KHFP11a,KHFP11b] analysis of the stability of magnetic phases (series expansion and quantum Monte-Carlo), finite region without any long-range order is detected (quantum Monte-Carlo), topological order is excluded (exact diagonalization) statistical mechanics…”

“…The main content of this chapter was published under the same title in Physical Review B [KHFP11a]. Some additional notes were later published in the proceedings for the conference on strongly correlated electron systems (SCES 2011) [KHFP11b] with the same coauthors: Sebastian Fuchs who implemented some crucial improvements to the quantum Monte-Carlo code that was used for the simulations, Andreas Honecker as scientific advisor who performed the third-and fourth-order series expansion and Thomas Pruschke as additional scientific advisor.…”