Condensed Matter Theory

Abstract:

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions (2D), especially in models of closely packed arrays of 1D quantum wires, each being described as a LL. Such coupled-wire models have been successfully used to construct 2D anisotropic non-Fermi liquids, quantum Hall states, topological phases, and quantum spin liquids. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moir\'e superlattice made of twisted bilayer tungsten ditelluride (tWTe$_{2}$). Originating from the anisotropic lattice of the monolayer, the moir\'e pattern of tWTe$_{2}$ hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tunable by the interlayer twist angle. At a twist angle of ~ 5 degrees, we find that hole-doped tWTe$_{2}$ exhibits exceptionally large transport anisotropy with a resistance ratio of ~ 1000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviors, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Abstract:

We study classical percolation models in Fock space as proxies for the quantum many-body localisation (MBL) transition. Percolation rules are defined for two models of disordered quantum spin-chains using their microscopic quantum Hamiltonians and the topologies of the associated Fock-space graphs. The percolation transition is revealed by the statistics of Fock-space cluster sizes, obtained by exact enumeration for finite-sized systems. As a function of disorder strength, the typical cluster size shows a transition from a volume law in Fock space to sub-volume law, directly analogous to the behaviour of eigenstate participation entropies across the MBL transition. Finite-size scaling analyses for several diagnostics of cluster size statistics yield mutually consistent critical properties. We show further that local observables averaged over Fock-space clusters also carry signatures of the transition, with their behaviour across it in direct analogy to that of corresponding eigenstate expectation values across the MBL transition. The Fock-space clusters can be explored under a mapping to kinetically constrained models. Dynamics within this framework likewise show the ergodicity-breaking transition via Monte Carlo averaged local observables, and yield critical properties consistent with those obtained from both exact cluster enumeration and analytic results derived in our recent work [arXiv:1812.05115]. This mapping allows access to system sizes two orders of magnitude larger than those accessible in exact enumerations. Simple physical pictures based on freezing of local real-space segments of spins are also presented, and shown to give values for the critical disorder strength and correlation length exponent $\nu$ consistent with numerical studies.