Finite Temperature

C. Daniel Freeman, C. M. Herdman, Dylan J Gorman +1 more

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a low-temperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.

Gerald Dennis Mahan

Garry Bowen, M. Gulácsi

Finite-temperature properties of a non-Fermi-liauid system is one of the most challenging problems in the current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liauids is in one dimension, where the concept of a Luttinger liauid has arisen. The existence of a critical point at zero temperature in one-dimensional systems, and the fact that experiments are all undertaken at finite temperatures, implies a need for these one-dimensional systems to be examined at finite temperatures. Accordingly, we extended the well-known bosonization method of one-dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite-temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.

Yun-fai Ching

Numerical studies of finite temperature properties of quantum spin models by Yun-fai Ching thesis 1996 xii, 56 leaves : ill. ; 30 cm We use the newly developed finite temperature Lanczos algorithm to calculate the finite temperature properties of quantum…Read more ›

Peter Fulde