14 problems

Let $T$ be a finite Abelian group, let $G$ be a finite symmetry group, and let $L$ be an MBL LIOM algebra in the MBL phase of the $T$-quantum-double model. Let $\mathcal{U}$ be a…

Let $Q_{d+1}^{(0)}$ denote the group of quantum cellular automaton classes that can preserve an on-site LIOM algebra, and let $d\geq1$ be the spatial dimension parameter. On-site-p…

Let $L$ be an MBL LIOM algebra in the toric-code MBL phase, meaning that it is related by a finite-depth circuit to the algebra generated by toric-code star and plaquette operators…

Let $G$ be a finite group, let $d$ be the spatial dimension, and let $Q_{d-p}$ denote the relevant group of quantum cellular automaton classes. An MBL Hamiltonian has trivial spont…

Consider the Floquet system defined by the Hamiltonian model in equation, with parameters $(\mathbf h,\mathbf J)\in[-20,20]^{\times(3N-1)}$. Discrete time-crystal stability conject…

Strong-disorder MPDLE conjecture. MPDLE holds in the regime of strong disorder. This conjecture concerns the decay of multi-point correlation functions and would extend two-point d…

Let the quantum generalized random energy model (QGREM) have multiple phase transitions, with critical field strengths denoted by $\Gamma_k$, and let $\pmb{\sigma_k}$ denote the co…

A Lieb–Robinson bound is a bound controlling the spatial propagation of operators under Hamiltonian time evolution; its lightcone describes the region that can be significantly aff…

An eigenstate is a state of the disordered many-body quantum system, and a finite-depth local circuit is a quantum circuit composed of a bounded number of layers of local unitary g…

Spins-$1/2$ are described by Pauli matrices $\sigma_i^\alpha$, and dressed ("tailed") spin operators $\tau_i^\alpha$ are operators associated with these degrees of freedom. Huse et…

Let $H(\omega)$ be the Hamiltonian of a disordered one-dimensional system of spins or fermions, and let sufficiently large disorder be fixed. A quasi-local unitary transformation i…

For an MBL system with $N$ degrees of freedom, assign its many-body eigenstates bijectively to binary strings $|i_{b1_1}i_{b1_2}cdots i_{b1_N}\rangle$, with $i_b1=\pm1$, and let…

Consider a classical chain of harmonic oscillators with random masses, augmented by an anharmonicity parameter $g$, and let $\kappa(g,\beta)$ denote its heat conductivity at invers…

Let $H$ be the random-field Ising-chain Hamiltonian on $L$ sites, with eigenfunctions $\Psi$, and let $S^{(3)}_{L/2}$ be the Pauli matrix at the central site. At infinite temperatu…