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arXiv:1303.0883 · Physical Review B

Disorder line and incommensurate floating phases in the quantum Ising model on an anisotropic triangular lattice

Vladimir Iglovikov, Richard T. Scalettar, Rajiv R. P. Singh, J. Oitmaa

Published Jun 13, 2013• 2 citations
arXivHTMLPDF

Abstract

We present a quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction $J$ and one diagonal second-neighbor interaction ${J}^{\ensuremath{'}}$, interpolating between square-lattice (${J}^{\ensuremath{'}}=0$) and triangular-lattice (${J}^{\ensuremath{'}}=J$) limits. At a transverse field of ${B}_{x}=J$, the disorder line first introduced by Stephenson [J. Math. Phys. 5, 1009 (1964)], where the correlations go from Neel to incommensurate, meets the zero-temperature axis at ${J}^{\ensuremath{'}}\ensuremath{\approx}0.7J$. Strong evidence is provided that the incommensurate phase at larger ${J}^{\ensuremath{'}}$, at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous quantum Monte Carlo work by Isakov and Moessner [Phys. Rev. B 68, 104409 (2003)] for the isotropic triangular lattice (${J}^{\ensuremath{'}}=J$). For the isotropic triangular lattice, we also obtain the entropy function and constant entropy contours using a mix of quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in the presence of a transverse field occur at very low entropy.

DOI
10.1103/physrevb.87.214415

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Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers $\ensuremath{\alpha}$ of the interactions. The phase boundary for the ferromagnet is obtained as a function of $\ensuremath{\alpha}$. For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization $(M,\ensuremath{-}\frac{M}{2},\ensuremath{-}\frac{M}{2})$ with unsaturated M<1M<1M<1 in a process known as ``order by disorder'' similar to the nearest-neighbor antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest-neighbor and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.
The anisotropic triangular nearest-neighbor Ising model, with antiferromagnetic interactions, is studied. The phase diagram, as a function of temperature and field, has a complex structure. Two commensurate ordered phases are found. The transition to one is Ising-type. The second is reached from the disordered phase in one of two ways: either via an intermediate uniaxial incommensurate phase---which is reached at high temperatures by a Kosterlitz-Thouless transition and at low temperatures undergoes an incommensurate-commensurate transition---or by a single continuous transition. The latter transition is in the same universality class as the chiral three-state Potts model, with thermal exponent within 4% of that of the three-state Potts model. These two transition regimes are found to be separated by a Lifshitz point. The phase diagram and critical behavior were determined by analytical (symmetry analysis and free-fermion approximation) as well as numerical (phenomenological renormalization-group and Monte Carlo) methods.
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We investigate the low-energy properties as well as quantum and thermal phase transitions of the Baxter-Wu model in a transverse magnetic field. Our study relies on stochastic series expansion quantum Monte Carlo and on series expansions about the low- and high-field limits at zero temperature using the quantum finite-lattice method on the triangular lattice. The phase boundary consists of a second-order critical line in the four-state Potts model universality class starting from the pure Baxter-Wu limit meeting a first-order line connected to the zero-temperature transition point (h≈2.4, T=0). Both lines merge at a tricritical point approximately located at (h≈2.3J, T≈J).