Equality of bulk wave functions and edge correlations in some topological superconductors: a spacetime derivation

Pseudo-fermion functional renormalization group for spin models

For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow ofm-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.

Wave function and strange correlator of short-range entangled states

We demonstrate the following conclusion: If |Ψ⟩ is a one-dimensional (1D) or two-dimensional (2D) nontrivial short-range entangled state and |Ω⟩ is a trivial disordered state defined on the same Hilbert space, then the following quantity (so-called "strange correlator") C(r,r('))=⟨Ω|ϕ(r)ϕ(r('))|Ψ⟩/⟨Ω|Ψ⟩ either saturates to a constant or decays as a power law in the limit |r-r(')|→+∞, even though both |Ω⟩ and |Ψ⟩ are quantum disordered states with short-range correlation; ϕ(r) is some local operator in the Hilbert space. This result is obtained based on both field theory analysis and an explicit computation of C(r,r(')) for four different examples: 1D Haldane phase of spin-1 chain, 2D quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2D spin-2 Affleck-Kennedy-Lieb-Tasaki state on the square lattice, and the 2D bosonic symmetry-protected topological phase with Z(2) symmetry. This result can be used as a diagnosis for short-range entangled states in 1D and 2D.