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Physical Review A

Orbital phases of p -band ultracold fermions in a frustrated triangular lattice

J. H. Wu, Hui Tan, Rui Cao, Jianmin Yuan, Yongqiang Li

Published Oct 23, 2024• 3 citations
Publisher

Abstract

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 $p$-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.

DOI
10.1103/physreva.110.043319

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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.
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.
Multi-orbital optical lattices have been attracting rapidly growing research interests in the last several years, providing fascinating opportunities for orbital-based quantum simulations. Here, we consider bosonic atoms loaded in the degenerate ppp-orbital bands of a two-dimensional triangular optical lattice. This system is described by a multi-orbital Bose-Hubbard model. We find the confined atoms in this system develop spontaneous orbital polarization, which forms a chiral Skyrmion lattice pattern in a large regime of the phase diagram. This is in contrast to its spin analogue which largely requires spin-orbit couplings. The emergence of the Skyrmion lattice is confirmed in both bosonic dynamical mean-field theory (BDMFT) and exact diagonalization (ED) calculations. By analyzing the quantum tunneling induced orbital-exchange interaction in the strong interaction limit, we find the Skyrmion lattice state arises due to the interplay of ppp-orbital symmetry and the geometric frustration of the triangular lattice. We provide experimental consequences of the orbital Skyrmion state, that can be readily tested in cold atom experiments. Our study implies orbital-based quantum simulations could bring exotic scenarios unexpected from their spin analogue.
Complex lattices provide a versatile ground for fascinating quantum many-body physics. Here, we propose an exotic mechanics for generating orbital frustration in hexagonal lattices. We study two-component (pseudospin-12\frac{1}{2}21​) Bose gases in ppp-orbital bands of two-dimensional hexagonal lattices, and find that the system exhibits previously untouched orbital frustration as a result of the interplay of spin and orbital degrees of freedom, in contrast to normal Ising-type orbital ordering of spinless ppp-orbital band bosons in two-dimensional hexagonal lattices. Based on the classification by symmetry analysis, we find the interplay of orbital frustration and strong interaction leads to exotic Mott and superfluid phases with spin-orbital intertwined orders, in spite of the complete absence of spin-orbital interaction in the Hamiltonian. Our study implies many-body correlations in a multiorbital setting could induce rich spin-orbital intertwined physics in complex lattice structures.
We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in the work of Mathey et al. [Phys. Rev. Lett. 97, 030601 (2006)]. Using functional renormalization-group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1∕21∕21∕2 fermions on an isotropic lattice we find a competition of sss-, ppp-, extended ddd-, and fff-wave symmetries, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended ppp-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between ppp- and fff-wave symmetries. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.
Quantum phases of sp2sp^2sp2-orbital bosonic gases in a hexagonal lattice
Orbital degree of freedom plays an important role for understanding quantum many-body phenomena. In this work, we study an experimentally related setup with ultracold bosons loaded into hybridized bands of two-dimensional hexagonal optical lattices. We find that the system supports various quantum many-body phases at zero temperature, including chiral superfluid and chiral Mott insulator by breaking time-reversal symmetry, and time-reversal-even insulating phase, based on dynamical mean-field theory. To explain the time-reversal-even phase, a fourth-order orbital-exchange model is derived to explain the underlying mechanics. To relate to experimental situations, we make band-structure calculations to obtain the Hubbard parameters, and show that these orbital ordering phases persist also in the presence of next-nearest-neighbor hopping.
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-metal-like atoms in optical lattices that can be effectively described by the two-band spin-1/21/21/2 Hubbard model including Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically ordered phases, which provides quantitative predictions for ongoing and future experiments aiming at approaching and studying long-range ordered states in optical lattices.