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arXiv:1211.4987 · Physical Review A

Simulation of frustrated classical XY models with ultracold atoms in three-dimensional triangular optical lattices

Arkadiusz Kosior, Krzysztof Sacha

Published Feb 4, 2013• 11 citations
arXivHTMLPDF

Abstract

Miscellaneous magnetic systems are currently being intensively investigated because of their potential applications in modern technologies. Nonetheless, a many-body dynamical description of complex magnetic systems may be cumbersome, especially when the system exhibits a geometrical frustration. This paper deals with simulations of the classical $XY$ model on a three-dimensional triangular lattice with anisotropic couplings, including an analysis of the phase diagram and a Bogoliubov description of the dynamical stability of mean-field stationary solutions. We also discuss the possibilities of the realization of Bose-Hubbard models with complex tunneling amplitudes in shaken optical lattices without breaking the generalized time-reversal symmetry and the opposite, i.e., real tunneling amplitudes in systems with the time-reversal symmetry broken.

DOI
10.1103/physreva.87.023602

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Miscellaneous magnetic systems are currently being intensively investigated because of their potential applications in modern technologies. Nonetheless, a many-body dynamical description of complex magnetic systems may be cumbersome, especially when the system exhibits a geometrical frustration. This paper deals with simulations of the classical XYXYXY model on a three-dimensional triangular lattice with anisotropic couplings, including an analysis of the phase diagram and a Bogoliubov description of the dynamical stability of mean-field stationary solutions. We also discuss the possibilities of the realization of Bose-Hubbard models with complex tunneling amplitudes in shaken optical lattices without breaking the generalized time-reversal symmetry and the opposite, i.e., real tunneling amplitudes in systems with the time-reversal symmetry broken.
Orbital degrees of freedom play an important role in understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into ppp-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Due to the interplay of anisotropic hoppings and geometrical frustration, a rich phase diagram is found, including stripe-orbital, paraorbital, and ferro-orbital phases, in contrast to its bosonic analog with orbital-skyrmion ordering in the identical lattice. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.
We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-1/2 XYXYXY-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin liquid phases predicted recently [Schmied et al., New J. Phys. {\bf 10}, 045017 (2008)].
Orbital phases of ppp-band ultracold fermions in the frustrated triangular lattice
Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into ppp-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Low-temperature phase diagrams are obtained, which contain stripe-, ferro- and para-orbital ordered quantum phases, due to the interplay of anisotropic hoppings and geometrical frustration. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.
Abstract Quantum antiferromagnets with geometrical frustration exhibit rich many-body physics but are hard to simulate by means of classical computers. Although quantum-simulation studies for analyzing such systems are thus desirable, they are still limited to high-temperature regions, where interesting quantum effects are smeared out. Here we propose a feasible protocol to perform analog quantum simulation of frustrated antiferromagnetism with strong quantum fluctuations by using ultracold Bose gases in optical lattices at negative absolute temperatures. Specifically, we show from numerical simulations that the time evolution of a negative-temperature state subjected to a slow sweep of the hopping energy simulates quantum phase transitions of a frustrated Bose–Hubbard model with sign-inverted hoppings. Moreover, we quantitatively predict the phase boundary between the frustrated superfluid and Mott-insulator phases for triangular lattices with hopping anisotropy, which serves as a benchmark for quantum simulation.
The modulation of an optical lattice potential that breaks time-reversal symmetry enables the realization of complex tunneling amplitudes in the corresponding tight-binding model. For a superfluid Fermi gas in a triangular lattice potential with complex tunnelings, the pairing function acquires a complex phase, so the frustrated magnetism of fermions can be realized. Bose-Fermi mixtures of bosonic molecules and unbound fermions in the lattice also show interesting behavior. Due to boson-fermion coupling, the fermions become enslaved by the bosons and the corresponding pairing function takes the complex phase determined by the bosons. In the presence of bosons the Fermi system can reveal both gapped and gapless superfluidity.
Magnetism plays a key role in modern technology and stimulates research in several branches of condensed matter physics. Although the theory of classical magnetism is well developed, the demonstration of a widely tunable experimental system has remained an elusive goal. Here, we present the realization of a large-scale simulator for classical magnetism on a triangular lattice by exploiting the particular properties of a quantum system. We use the motional degrees of freedom of atoms trapped in an optical lattice to simulate a large variety of magnetic phases: ferromagnetic, antiferromagnetic, and even frustrated spin configurations. A rich phase diagram is revealed with different types of phase transitions. Our results provide a route to study highly debated phases like spin-liquids as well as the dynamics of quantum phase transitions.