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Register a new userDetection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers
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Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states. We analytically show that the Chern number can be decomposed as a sum of component specific winding numbers, which are themselves physically observable. We apply this method to two systems, the quantum spin Hall insulator and a staggered topological superconductor, and show that (spin) Chern numbers are accurately reproduced. The measurements required for constructing the component winding numbers also enable one to probe the entanglement spectrum with respect to component partitions. Our method is particularly suited to experiments with cold atoms in optical lattices where time-of-flight images can give direct access to the relevant observables.
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The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wavefunctions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are non-vanished.
Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature $n$ particle species on $mathbb Z^d$. The PVBS models were originally introduced as toy models for the classification of ground state phases. A crucial ingredient for this classification is the existence of a spectral gap above the ground state sector. In this work, we derive a spectral gap for PVBS models at arbitrary species number $n$ and in arbitrary dimension $d$ in the perturbative regime of small anisotropy parameters. Instead of using the more common martingale method, the proof verifies a finite-size criterion in the spirit of Knabe.
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities play complementary roles: the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties can, in special cases, be deduced from the quantum metric. In this work, we establish general and exact relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. In particular, we demonstrate that topological indices (Chern numbers or winding numbers) are bounded by the quantum volume determined by the quantum metric. Our theoretical framework, which builds on the Clifford algebra of Dirac matrices, is applicable to topological insulators and semimetals of arbitrary spatial dimensions, with or without chiral symmetry. This work clarifies the role of the Fubini-Study metric in topological states of matter, suggesting unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
The Happer model, as the variation of Rabi-Breit model, describes the interactions between the total nuclear spin and the total electron spin-1 of the triplet dimer molecules of ${}^{87}text{Rb}$. One interesting physical consequence of the Happer model is its puzzling degeneracy. In this paper, under the periodic driven magnetic field on total electron spin, the topological properties of the Happer model are present. Specifically, we calculate the Chern number of the system, both for the non-degenerate and degenerate cases. We show that the Chern number is closely related to the total angular momentum of the system, instead of the electron spin. Furthermore, the perturbing spin-axis interaction term is also introduced for detecting the influence on the corresponding topological Chern number. At last, in momentum space, we compare the Happer model with the topological semimetal in the sense of topological numbers. In such model, a magnetostatic shielding --like phenomena occurs.
The recent realizations of topological valley phase in photonic crystal, an analog of gapped valleytronic materials in electronic system, are limited to the valley Chern number of one. In this letter, we present a new type of valley phase that can have large valley Chern number of two or three. The valley phase transitions between the different valley Chern numbers (from one to three) are realized by changing the configuration of the unit cell. We demonstrate that these new topological phases can guide the wave propagation robustly along the domain wall of sharp bent. Our results are promising for the exploration of new topological phenomena in photonic systems.
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