Quantum Glassiness

Abstract

Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. This paper presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.

Figures (1)

• Figure 1: (a) Cubic cell of an fcc lattice. The centers of the six faces form an octahedron, with its sites labeled from 1 (topmost) to 6. In addition to the set of octahedra formed by the face centered sites, there are three more sets of octahedra that can be assembled from sites both on faces and on corners of the cubic cells, totaling 4 such sets. Six-spin operators are defined on these octahedra using the $\sigma^{\rm x,y,z}$ components of spin on each vertex as described in the text. (b) Centers of 6 octahedra cells that share a spin, which resides at the site $\tilde{I}$ shown at the center. The x,y, or z labels sitting at the centers of the octahedra show which spin operator $\sigma^{\rm x,y,z}_{\tilde{I}}$ flip their $O_I$ eigenvalue. Acting with any of the operators $\sigma^{\rm x,y,z}_{\tilde{I}}$ always flip the eigenvalues $O_I$ of exactly four octahedra.