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One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
We propose a quantum Hamiltonian for a transmission line with charge discreteness. The periodic line is composed of an inductance and a capacitance per cell. In every cell the charge operator satisfies a nonlinear equation of motion because…
One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is…
We present a symmetric LDPC code with constant rate and constant distance (i.e. good LDPC code) that its constraint space is generated by the orbit of one constant weight constraint under a group action. Our construction provides the first…
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…
Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of…
The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including…
The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here…
Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a…
Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $\beta=1=\nu=\eta$ whereas the same on a ladder belong to directed percolation (DP)universality. We conjecture…
Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
We construct quasilocal conserved charges in the gapless ($|\Delta| \le 1$) regime of the Heisenberg $XXZ$ spin-$1/2$ chain, using semicyclic irreducible representations of $U_q(\mathfrak{sl}_2)$. These representations are characterized by…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…
The quantum dimer and loop models attract great attentions, partially because the fundamental importance in the phases and phase transitions emerging in these prototypical constrained systems, and partially due to their intimate relevance…
Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection…
A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes…
Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix…