In recent years we have seen the birth of a new field known as Hamiltonian complexity lying
at the crossroads between computer science and theoretical physics. Hamiltonian …

We study Quantum Many-Body Scars (QMBS) in the language of commutant algebras,
which are defined as symmetry algebras of families of local Hamiltonians. This framework …

Frustration-free (FF) spin chains have a property that their ground state minimizes all
individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF …

For families of Hamiltonians defined by parts that are local, the most general definition of a
symmetry algebra is the commutant algebra, ie, the algebra of operators that commute with …

The spectral gap problem—determining whether the energy spectrum of a system has an
energy gap above ground state, or if there is a continuous range of low-energy excitations …

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role
for distinguishable particles in scenarios such as entanglement characterization, theory of …

The nature of entanglement in many-body systems is a focus of intense research with the
observation that entanglement holds interesting information about quantum correlations in …

In quantum many-body systems, the existence of a spectral gap above the ground state has
far-reaching consequences. In this paper, we discuss “finite-size” criteria for having a …

Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean
satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local …

Symmetry algebras of quantum many-body systems with locality can be understood using
commutant algebras, which are defined as algebras of operators that commute with a given …