17 problems

A two-dimensional PEPS has a bulk Hamiltonian and a corresponding one-dimensional boundary Hamiltonian. The bulk Hamiltonian is gapped when it has a spectral gap above its ground-s…

A lattice system is equipped with a symmetry and an associated anomaly, and its possible quantum phases of matter are those that can emerge in the lattice system. Emergibility hypo…

Let … be the Ising Rokhsar–Kivelson state on the $d$-dimensional hypercubic lattice, where $\mathcal N$ normalizes the state and the product is over nearest-neighbor pairs. Here…

Let good quantum low-density parity-check (LDPC) codes be defined on expander graphs, with the associated Hamiltonians given by sums of products of a bounded number of Pauli matric…

Let a crystallographic group $G$ act on a lattice, and let a symmetric short-range-entangled phase (sym-SRE phase) mean a phase preserving the symmetry and having no intrinsic long…

Let $|\phi\rangle$ and $|\psi\rangle$ be quantum states, and let their entropy excess be the difference between the corresponding pseudo-entropy or SVD entropy and the average of t…

Let $S^{\phi|\psi}_{\mathrm{P}}$ denote the pseudo-entropy of two quantum states $|\phi\rangle$ and $|\psi\rangle$, and let $S^{\phi|\psi}_{\mathrm{P}}$ have excess … where…

Anyonic characterization conjecture. Two ground states are in the same phase if and only if their associated anyons behave identically.

Let a quantum system be in an ordered phase in which a microscopic symmetry is spontaneously broken, and let the ordered phase have emergent higher-form or non-invertible symmetrie…

Consider a two-dimensional spin system with a net of boundary algebras obtained from a net of projections. The topological order of the bulk is the algebraic data describing its bu…

Let the Lee-Yang C-weak Hopf algebra be the algebra described in Example, and let the associated RFP MPDOs be the renormalization fixed-point matrix product density operators const…

Let RFP MPDOs be the renormalization fixed-point matrix product density operators constructed from biconnected C-weak Hopf algebras. The general phase classification of these state…

A gapped quantum liquid phase is described by an equivalence class of lattice models, and let the space of models be the parameter space of such lattice realizations. Path-connecte…

Commuting frustration-free representative conjecture. For a very large class of physical systems, there is a commuting, frustration-free Hamiltonian in the same phase; this Hamilto…

In one-dimensional systems, consider topological phases and their associated ground states, together with adiabatic deformations that may or may not preserve a given symmetry. Symm…

Consider the model of two-dimensional STS Hamiltonians, whose logical operators can have pairs of zero-dimensional and two-dimensional geometric shapes, as in a classical ferromagn…

Let $H_A$ and $H_B$ be two-dimensional STS models. Denote their numbers of logical qubits by $k^{(A)}$ and $k^{(B)}$, and their numbers of zero-dimensional logical operators by…