Zhengzhi Wu

Abstract:

While experimental evidence for spacetime supersymmetry (SUSY) in particle physics remains elusive, condensed matter systems offer a promising arena for its emergence at quantum critical points (QCPs). Although there have been a variety of proposals for emergent SUSY at symmetry-breaking QCPs, the emergence of SUSY at fractionalized QCPs remains largely unexplored. Here, we demonstrate emergent spacetime SUSY at a fractionalized QCP in the Kitaev honeycomb model with Su-Schrieffer-Heeger (SSH) spin-phonon coupling. Specifically, through numerical computations and analytical analysis, we show that the anisotropic SSH-Kitaev model hosts a fractionalized QCP between a Dirac spin liquid and an incommensurate or commensurate valence-bond-solid phase coexisting with Z_{2} topological order. A low-energy field theory incorporating phonon quantum fluctuations reveals that this fractionalized QCP features an emergent N=2 spacetime SUSY. We further discuss their universal experimental signatures in thermal transport and viscosity, highlighting the concrete lattice realization of emergent SUSY at a fractionalized QCP in 2D.

Abstract:

We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several alternative boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a (1+1) dimensional conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena.

Abstract:

The nonintegrable higher spin Kitaev honeycomb model has an exact Z_{2} gauge structure, which exclusively identifies quantum spin liquid in the half-integer spin Kitaev model. But its constraints for the integer-spin Kitaev model are much limited, and even trivially gapped insulators cannot be excluded. The physical implications of exact Z_{2} gauge structure, especially Z_{2} fluxes, in integer-spin models remain largely unexplored. In this Letter, we theoretically show that a spin-S Yao-Lee model [a spin-orbital model with SU(2) spin-rotation symmetry] possesses a topologically nontrivial quantum spin-orbital liquid ground state for any spin (both integer and half-integer spin) by constructing exact deconfined fermionic Z_{2} gauge charges. We further show that the conserved Z_{2} flux can also demonstrate the intriguing spin fractionalization phenomena in the non-Abelian topological order phase of the spin-1 Yao-Lee model. Its deconfined Z_{2} vortex excitation carries fractionalized spin-1/2 quantum number in the low-energy subspace, which is also a non-Abelian anyon. Our exact manifestation of spin fractionalization in an integer-spin model is rather rare in previous studies, and is absent in the Kitaev honeycomb model.

Abstract:

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.

Abstract:

We theoretically show that in the presence of conventional or higher order Van Hove singularities (VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux 3φ in each triangular plaquette at φ=π/3 and π/6 in moiré systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state under certain conditions through the renormalization group calculation and a flux insertion argument. Moreover, we also find that a topological nontrivial loop current order becomes the leading instability if the Fermi surface with conventional VHS is perfectly nested at φ=π/3. Similar to the Haldane model, this loop current state has the quantum anomalous Hall effect. If we dope this loop current state or introduce a finite next-nearest-neighbor hopping t′, the chiral d-wave PDW becomes the dominant instability. Experimentally, the flux can be effectively tuned by an out-of-plane electric field in moiré systems based on graphene and transition metal dichalcogenides.