Spotting quantum scars on the complex plane
Some interacting quantum systems are so stubborn that they refuse to thermalize. There is yet a consensus on whether there is a universal mechanism responsible for these “scars.” Previously to spot a scar one must examine the individual quantum states. We demonstrate another way to detect and diagnose the scars using Fisher zeros, i.e., the zeros of the partition function on the complex inverse temperature plane. For systems with scars, a mountain range of Fisher zeros will appear off the imaginary axis, separating the plane into regions with distinctive thermalization behaviors. (In the map above, each “glacial peak” corresponds to a zero and the dark blue “river” corresponds to a fixed line in renormalization group). This stat mech approach generalizes the pioneering work of Lee, Yang, and Fisher on thermal phase transitions to the realm of far-from-equilibrium dynamics.
Phys. Rev. Lett. 135, 070402 (2025).
\(f\)-wave superfluidity: the pairing glue and the missing thumb
We predict that the dominant pairing channel is \(f\)-wave in a two-dimensional Rydberg-dressed Fermi gas. How can repulsive interaction serve as the pairing glue? Why \(f\)-wave, and what happens to the \(p\)-wave? How does the physics here differ from the Kohn-Luttinger mechanism? We raise and address these questions in the following two papers.
Phys. Rev. B 109, 054519 (2024); Phys. Rev. A 101, 023624 (2020).
Making sense of non-Hermitian Chern Insulators
In contrast to their Hermitian cousins, non-Hermitian Chern insulators exhibit rich and confounding edge spectra in strip geometry, in apparent violation of the bulk-edge correspondence. We restore the correspondence and show the edge phase diagram can be understood algebraically using the notion of generalized Brillouin zone. A dozen theorems are proved to bring two non-Hermitian generalizations of the Qi-Wu-Zhang model under analytical control.
Phys. Rev. B 107, 035101 (2023).
The rise and fall of plaquette order
We revisit the ground-state phase diagram of the Shastry-Sutherland model using high resolution functional renormalization group that tracks the flows of over 50 million running couplings. The well known phases of singlet dimer and Neel order are captured accurately. Moreover, we observe clear signals for the rise, and then downfall of the plaquette order, before the onset of the Neel order. This points to a finite spin liquid region where the flow is continuous without any indication of divergence.
Phys. Rev. B 105, L041115 (2022).
Knots and non-Hermitian Bloch Bands
We prove that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian Hamiltonians with separable bands. The transition between two phases characterized by distinct knots occur through exceptional points. This is illustrated by a simple “twister model.” An algorithm is designed to construct the tight-binding Hamiltonian for any desired knot, e.g. the Hopf link, the trefoil knot, and the figure-8 knot.
Phys. Rev. Lett. 126, 010401 (2021).
Topological invariant for quantum quench
We introduce the concept of loop unitary and show its homotopy invariant characterizes the dynamical topology of the quench dynamics of band insulators. A theorem is proved: the invariant equals the change in Chern number across the quench, \(W_3= C_f-C_i\).
Phys. Rev. Lett. 124, 160402 (2020). [Editors’ Suggestions]
Higher-order topological phases by periodic driving
How to dynamically generate higher-order topological phases with zero- and π-corner modes? We illustrate a scheme by two examples: the Floquet quadrupole and octupole insulators. A pair of \(Z_2\) invariants are introduced to fully characterize these Floquet phases.
Phys. Rev. Lett. 124, 057001 (2020).
Topological circuits of inductors and capacitors
Loops, stars, and ladder with a twist. Build your own topological circuits and witness the bulk-boundary correspondence, connections, monopoles and 2nd Chern number.
Annals of Physics 399, 289 (2018).
Functional renormalization group
We solve the dipolar Heisenberg model on triangular lattice using pseudo-fermion functional renormalization group. The \(120^\circ\) order is found melted completely and give way to a wide region of quantum paramagnetic phase with no magnetic long range order.
Phys. Rev. Lett. 120, 187202 (2018).
Tensor network for quantum spin models
We solve the dipolar Heisenberg model on square lattice using tensor network algorithms. Its phase diagram contains the Neel, stripe, spiral, and a quantum paramagnetic phase. Is it a spin liquid?
Phys. Rev. Lett. 119, 050401 (2017).