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Physical review. B./Physical review. B

Magnetism driven by the interplay of fluctuations and frustration in the easy-axis triangular XXZ model with transverse fields

Daisuke Yamamoto, Giacomo Marmorini, Masahiro Tabata, Kazuki Sakakura, Ippei Danshita

Published Oct 21, 2019• 32 citations
Publisher

Abstract

We study the combined effects of fluctuations and frustration in frustrated antiferromagnets described by the spin-1/2 easy-axis XXZ model with transverse magnetic fields, and propose its promising quantum simulation with a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.

DOI
10.1103/physrevb.100.140410

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We study the combined effects of fluctuations and frustration in frustrated antiferromagnets described by the spin-1/2 easy-axis XXZ model with transverse magnetic fields, and propose its promising quantum simulation with a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.
Quantum simulators based on cold atomic gases can provide an ideal platform to study the microscopic mechanisms behind intriguing properties of solid materials and further explore novel exotic phenomena inaccessible by chemical synthesis. Here we propose and theoretically analyze a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice as a promising realization of synthetic frustrated antiferromagnets. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a novel spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.
We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the three-dimensional XY universality class.
The triangular lattice of S=1/2 spins with XXZ anisotropy is a ubiquitous model for various frustrated systems in different contexts. We determine the quantum phase diagram of the model in the plane of the anisotropy parameter and the magnetic field by means of a large-size cluster mean-field method with a scaling scheme. We find that quantum fluctuations break up the nontrivial continuous degeneracy into two first-order phase transitions. In between the two transition boundaries, the degeneracy-lifting results in the emergence of a new coplanar phase not predicted in the classical counterpart of the model. We suggest that the quantum phase transition to the nonclassical coplanar state can be observed in triangular-lattice antiferromagnets with large easy-plane anisotropy or in the corresponding optical-lattice systems.
We report on a systematic study of two-dimensional, periodic, frustrated Ising models with quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagom\'e lattice antiferromagnets, fully frustrated models on the square and hexagonal (honeycomb) lattices, a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice antiferromagnet, as well as two quasi-one-dimensional lattices that have considerable pedagogical value. All of these exhibit a macroscopic degeneracy at T=0T=0T=0 in the absence of the transverse field, which enters as a singular perturbation. We analyze these systems with a combination of a variational method at weak fields, a perturbative Landau-Ginzburg-Wilson approach from large fields, as well as quantum Monte Carlo simulations utilizing a cluster algorithm. Our results include instances of quantum order arising from classical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder arising from classical disorder (kagom\'e). We also discuss the effect of finite temperature, as well as the interplay between longitudinal and transverse fields---in the kagom\'e problem the latter gives rise to a nontrivial phase diagram with bond-ordered and bond-critical phases in addition to the disordered phase. We also note connections to quantum-dimer models and thereby to the physics of Heisenberg antiferromagnets in short-ranged resonating valence-bond phases that have been invoked in discussions of high-temperature superconductivity.
A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at 1/31/31/3 or 2/32/32/3-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at 1/21/21/2 filling. At finite temperature, U(1)\mathrm{U}(1)U(1) symmetry is emergent at 1/21/21/2 filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.