We present a proposal to realize and detect topological phase transition in optical lattices with alkaline-earth-metal atoms. Using state-dependent lattices and laser-assisted tunneling, we realize a dimerized spin- $1/2$ antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.We present a proposal to realize and detect topological phase transition in optical lattices with alkaline-earth-metal atoms. Using state-dependent lattices and laser-assisted tunneling, we realize a dimerized spin-$1/2$ antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.

Physical Review AOct 11, 20191 citation

Boundary-Obstructed Topological Superfluids in Staggered Spin-Orbit Coupled Fermi Gases

Yu‐Biao Wu, Guang‐Can Guo, Zhen Zheng +1 more

We present an experimental feasible proposal for synthesizing second-order topological superfluids that support Majorana corner modes in spin-orbit coupled Fermi gases. For this purpose, we consider the staggered spin-orbit coupling introduced in one direction. This results in a system consisted of two sublattices, providing extra degree of freedom for the emergent higher-order topological state. We find the topological trivial superfluids, first-order topological superfluids and boundary-obstructed second-order topological superfluids, as well as different topological phase transitions among them with respect to the the experimental tunable parameters. At the weak interaction regime, the phase transition is characterized by the Chern number accompanied by the bulk gap closing and reopening. However, at the strong interaction regime, we find the system can support the boundary-obstructed topological superfluids with Majorana corner modes, but topological phase transition dose not undergo the gap-closing of bulk bands. Instead the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge-state. The proposal is simply based on the $s$ -wave interaction and readily feasible via existing experimental techniques, which suggests new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superfluids in a simple but realistic microscopic model.We present an experimental feasible proposal for synthesizing second-order topological superfluids that support Majorana corner modes in spin-orbit coupled Fermi gases. For this purpose, we consider the staggered spin-orbit coupling introduced in one direction. This results in a system consisted of two sublattices, providing extra degree of freedom for the emergent higher-order topological state. We find the topological trivial superfluids, first-order topological superfluids and boundary-obstructed second-order topological superfluids, as well as different topological phase transitions among them with respect to the the experimental tunable parameters. At the weak interaction regime, the phase transition is characterized by the Chern number accompanied by the bulk gap closing and reopening. However, at the strong interaction regime, we find the system can support the boundary-obstructed topological superfluids with Majorana corner modes, but topological phase transition dose not undergo the gap-closing of bulk bands. Instead the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge-state. The proposal is simply based on the $s$-wave interaction and readily feasible via existing experimental techniques, which suggests new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superfluids in a simple but realistic microscopic model.

Jul 31, 20202 citations

Dynamical classification of topological quantum phases

Lin Zhang, Long Zhang, Sen Niu +1 more

arXiv:1802.10061中国科学通报：英文版Sep 29, 2018150 citations

Research Progress of Topological Quantum Materials: From First-Order to Higher-Order

Bing Liu, Wenjun Zhang

The exploration of topologically nontrivial states in condensed matter systems, along with their novel transport properties, has garnered significant research interest. This review aims to provide a comprehensive overview of representative topological phases, starting from the initial proposal of the quantum Hall insulator. We begin with a concise introduction, followed by a detailed examination of first-order topological quantum phases, including gapped and gapless systems, encompassing relevant materials and associated phenomena in experiment. Subsequently, we delve into the realm of exotic higher-order topological quantum phases, examining both theoretical propositions and experimental findings. Moreover, we discuss the mechanisms underlying the emergence of higher-order topology, as well as the challenges involved in experimentally verifying materials exhibiting such properties. Finally, we outline future research directions. This review not only systematically surveys various types of topological quantum states, spanning from first-order to higher-order, but also proposes potential approaches for realizing higher-order topological phases, thereby offering guidance for the detection of related quantum phenomena in experiments.The exploration of topologically nontrivial states in condensed matter systems, along with their novel transport properties, has garnered significant research interest. This review aims to provide a comprehensive overview of representative topological phases, starting from the initial proposal of the quantum Hall insulator. We begin with a concise introduction, followed by a detailed examination of first-order topological quantum phases, including gapped and gapless systems, encompassing relevant materials and associated phenomena in experiment. Subsequently, we delve into the realm of exotic higher-order topological quantum phases, examining both theoretical propositions and experimental findings. Moreover, we discuss the mechanisms underlying the emergence of higher-order topology, as well as the challenges involved in experimentally verifying materials exhibiting such properties. Finally, we outline future research directions. This review not only systematically surveys various types of topological quantum states, spanning from first-order to higher-order, but also proposes potential approaches for realizing higher-order topological phases, thereby offering guidance for the detection of related quantum phenomena in experiments.

SymmetryAug 26, 20238 citations

Topological Phases in the Quantum Theory.

Tom D. Imbo

Jan 1, 198839 citations

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antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.

s

-wave interaction and readily feasible via existing experimental techniques, which suggests new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superfluids in a simple but realistic microscopic model.