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Bulletin of the American Physical Society

Application of The Density Matrix Renormalization Group Algorithm to Classical Driven Diffusive Systems in One and Two Dimensions

Phillip Helms, Garnet Kin‐Lic Chan

Published Mar 7, 2018• 0 citations
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I begin, in chapter 2, by discussing the DMRG algorithms.The infinite-system algorithm and finite-system algorithm will be introduced. In chapter 3, coupled oscillators in one and two dimensions will be discussed in detail. As a bridge between bosonic and fermionic systems, I will consider the coherent- state treatment for solvable bosons in chapter 4. In chapter 5 the solvable fermionic systems in one and two dimension will be the subject. As an application, in chapter 6, the Ising plane with line-like defects will be treated using the transfer-matrix DMRG. Chapter 7, finally, contains a summary of the main results.
Abstract We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two tensor-network algorithms, namely, density matrix renormalization group and time evolving block decimation, are respectively implemented. The cumulant generating function for the current is numerically calculated and then compared with the analytical solution. Excellent agreement is found, manifesting the validity of these approaches in such an application. Moreover, the fluctuation theorem for the current is shown to hold.