Momentum polarization: an entanglement measure of topological spin and chiral central charge

Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure

Higher-order properties and Bell-inequality violation for the three-mode enhanced squeezed state

By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda (Q_{1}P_{2}+Q_{2}P_{1}) ]$ to the three-mode squeezing operator $S_{3}=\exp {i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]}$, we obtain the corresponding three-mode squeezed coherent state. The state's higher-order properties, such as higher-order squeezing and higher-order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement comparing with the usual cases. In addition, we examine the violation of Bell-inequality for the three-mode squeezed states by using the formalism of Wigner representation

Probing ultralight dark fields in cosmological and astrophysical systems

Dark matter constitutes $26\%$ of the total energy in our universe, but its nature remains elusive. Among the assortment of viable dark matter candidates, particles and fields with masses lighter than $40 \mathrm{eV}$, called ultralight dark matter, stand out as particularly promising thanks to their feasible production mechanisms, consistency with current observations, and diverse and testable predictions. In light of ongoing and forthcoming experimental and observational efforts, it is important to advance the understanding of ultralight dark matter from theoretical and phenomenological perspectives: How does it interact with itself, ordinary matter, and gravity? What are some promising ways to detect it? In this thesis, we aim to explore the dynamics and interaction of ultralight dark matter and other astrophysically accessible hypothetical fields in a relatively model-independent way. Without making specific assumptions about their ultraviolet physics, we first demonstrate a systematic approach for constructing a classical effective field theory for both scalar and vector dark fields and discuss conditions for its validity. Then, we explore the interaction of ultralight dark fields, both gravitational and otherwise, within various contexts such as nontopological solitons, neutron stars, and gravitational waves.Comment: PhD thesi