Condensed Matter Theory

Abstract:

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures - qualitative and quantitative - of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.

Abstract:

We establish twisted SnSe₂ as a tunable platform for simulating dimension-dependent correlated physics, distinct from conventional K-valley moiré systems. By constructing interacting Wannier models, we show that the stacking configuration dictates the effective lattice geometry. In AAstacked bilayers, a momentum-space nonsymmorphic symmetry constrains the single-particle hopping within each valley to be effectively one-dimensional, while still allowing fully two-dimensional interactions, thereby giving rise to an effective quasi-one-dimensional system. This dimensional reduction stabilizes exotic phases including dimerized states with finite residual entropy, valence bond solids, and quantum paramagnetism. Conversely, AB-stacking maps to a frustrated Kagome lattice; here, strong interactions drive the emergence of a classical spin liquid. The high tunability of this moiré system, which allows control over both the filling and interaction strength (via twist angle), renders twisted SnSe₂ a versatile platform for realizing a wide range of exotic correlated quantum phases.

Abstract:

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility $\chi(T)$ of an exactly solvable $S=1/2$ model on the decorated honeycomb lattice with quenched bond disorder and/or vacancies, leading to $\chi(T) = {\mathcal C}/T+ {\mathcal D} T^{\alpha(T) - 1}$ where $\alpha(T) \rightarrow 0$ as $T \rightarrow 0$. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder (with different $\alpha(T)$ in the two cases) is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

Abstract:

We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Renyi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Renyi entropies. Our results apply to both homogeneous and inhomogeneous quenches.