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arXiv:1908.04134 · Communications Physics

Frustrated quantum magnetism with Bose gases in triangular optical lattices at negative absolute temperatures

Daisuke Yamamoto, Takeshi Fukuhara, Ippei Danshita

Published Mar 20, 2020• 15 citations
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Abstract

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.

DOI
10.1038/s42005-020-0323-5

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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.
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)].
The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction Uc/t=7.0(2){U}_{c}/t=7.0(2)Uc​/t=7.0(2) and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully frustrated honeycomb lattice Bose–Hubbard model in the hard-core limit using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the nearest-neighbor interaction spatially around each lattice hexagon. A superfluid-to-Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken half-filled valence-bond solid state. When the interaction is forced to have no regular pattern, the insulating state is found to be random and gapped, suggesting the existence of a Mott glass phase.
Using the discrete truncated Wigner approximation (dTWA), we investigate the nonequilibrium dynamics of ultracold bosons confined in optical kagome lattices, focusing on both unfrustrated positive and frustrated negative hopping regimes. We consider a protocol in which the system is initialized in a Mott insulating state at unit filling, and the hopping amplitude is gradually increased from zero. For positive hopping, the melting of the Mott insulator is accompanied by the emergence of a sharp peak in the momentum distribution at the ΓΓΓ point of the lowest band, signaling the onset of superfluidity. In contrast, for negative hopping, the Mott insulator melts into a highly nontrivial state without long-range phase coherence, characterized instead by a broad momentum distribution within the flat band, consistent with recent experimental observations. These results demonstrate the applicability of dTWA to highly frustrated quantum systems and offer a new route for numerically exploring the dynamics of frustrated quantum magnets.
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bond solid state. When the interaction is forced to have no regular pattern, the Mott insulating phase is found to be featureless and gapped, making it an interesting candidate state for a quantum spin liquid arising in a Hamiltonian with only nearest-neighbor interactions.
Analog quantum simulation provides a unique toolkit to investigate quantum many-body problems of whose solutions may be incredibly challenging. In particular, using ultracold fermionic atoms in optical lattices it realizes the Fermi Hubbard model, which is a fundamental model in condensed matter physics exhibiting properties relevant to many intriguing strongly-correlated systems. However, most quantum simulators of the Hubbard model have so far restricted to the square geometries. In addition, access to low temperatures where the exotic quantum phases are predicted to develop has still remained elusive. In this thesis, we engineer a novel optical lattice with dynamically tunable geometries and significantly reduced technical noises. We extend for the first time the study of quantum magnetism into the exotic phases in a Fermi Hubbard system with tunable geometric frustration. As we continuously tune our system from a square to a triangular lattice geometry, we observe a transition from a Néel antiferromagnet to a 120-degree spin spiral state. We then study, again for the first time, how doping affects a frustrated quantum magnet. To our surprise, we found an emergent ferromagnetic state with strong particle doping, which is absent on the hole-doped side and is in stark contrast with the particle-hole symmetric doping dependence in a square lattice. To shed light on the role of itinerant dopants in the emergence of these new magnetic properties, we furthermore leverage the unique single-particle resolution capabilities of our platform to probe higher-order density and spin correlations. These measurements hint at a new type of magnetism induced by kinetic frustration, which manifests as local antiferromagnetic correlations around hole dopants and and ferromagnetic correlations around particle dopants. Unlike magnetism induced by exchange or superexchange interactions, the energy associated with this mechanism is the kinetic energy, closely related to the famous rigorous results by Nagaoka. Furthermore, the dynamical tunability of the lattice allows adibatic engineering of quantum states in optical lattices. We discuss the preliminery efforts to prepare strongly-correlated states with significantly reduced temperatures, which may pave the way towards low temperature states in the Hubbard model.