We propose new entanglement quantities for the non-Hermitian quantum systems which can correctly characterize the properties of the ground states of non-Hermitian systesm. We refer these entanglement quantities to the generic entanglement/Renyi entropy as shown in the left equations. We apply the generic entanglement/Renyi entropy to several models including the PT symmetric SSH model and the q-deformed XXZ model and find their central charges can be correctly obtained from our proposed entanglement quantities. 

Yi-TIng Tu, Yu-Chin Tzeng, Po-Yao Chang, Rényi entropies and negative central charges in non-Hermitian quantum systems, SciPost Phys. 12, 194 (2022).

Quantum entanglement characterizes the topological properties of topological systems. We propose a method to compute and study the entanglement entropy and spectrum in non-Hermitian systems. We find the existence of mid-gap states in the entanglement spectrum in the non-Hermitian Su-Schrieffer-Hegger (SSH) model with PT symmetry can determine the topology in this system. Moreover, at the critical point in this system, the entanglement entropy has a logarithmic scaling with corresponding central charge c=-2, which can be attributed to the non-unitary conformal field theory.

Po-Yao Chang, Jhih-Shih You, Xueda Wen, Shinsei Ryu, Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories, Phys. Rev. Research 2, 033069 (2020).

Thermalization in close quantum systems is not well understood. One possible route to tackle this problem is from understanding how the information/entanglement scrambled. Here, we use a quantum statistical model (random unitary circiuts) to observe the early time evolution of the entanglement. We find the local feature of the entanglement spectrum shows universal behavior in the early time stage, described by the random matrix theory. On the other hand, the globle feature of the entanglement spectrum is detected from the spectrum form factor. Our finding provides an insight of the early stage equilibration in closed quantum systems.

Po-Yao Chang, Xiao Chen, Sarang Gopalakrishnan, Jedediah H. Pixley, Evolution of entanglement spectra under generic quantum dynamics, Phys. Rev. Lett. 123, 190602 (2019).

We construct several non-equilibrium phases carrying non-trivial topological properties from quantum quench protocol. Besides the non-equilibrium topological Hopf insulators in three dimensions, we find a four dimensional quantum Hall state which can be realized in our setup. All the topological properties can be detected by the entanglement spectrum, which shows mid-gap states (crossings/Dirac cones/rings) if the phases are non-trivial.

Po-Yao Chang, Topology and entanglement in quench dynamics,  Phys. Rev. B 97, 224304 (2018).

When crystalline symmetries meet with topology, new features emerge. In CeNiSn, we find the nonsymmotrphic symmetry can give rise a topological protected surface state with a Mobius twist. This opens a new possibility of probing the crystalline topological properties in stronly correlated materials.

Po-Yao Chang, Onur Erten, Piers Coleman, Mobius Kondo Insulators,  Nature Physics 13, 794-798 (2017).

Due to strong correlations, spin can be fractionalized into charge neutral (Majorana) Fermions. We construct a theory, where the a neutral Fermi surface emerges in a Kondo systems. The order parameter in the long wavelenght theory has a Skrymion texture, which leads to the topological failure of superflow. We apply this concept to explain the bizzard behavior in SmB6, which is an insulator but has linear specific heat and quantum ossilations.

Onur Erten, Po-Yao Chang, Piers Coleman, Alexei Tsvelik, Skyrme insulators: insulators at the brink of superconductivity, Phys. Rev. Lett. 119, 057603 (2017).