Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP
arXiv:2110.08283 · doi:10.1088/1367-2630/ac4ee1
Abstract
We investigate how particle pair creation and annihilation, within the quantum transverse XY model, affects the non-equilibrium steady state (NESS) and Liouvillian gap of the stochastic Totally Asymmetric Exclusion Process (TASEP). By utilising operator quantization we formulate a perturbative description of the NESS. Furthermore, we estimate the Liouvillian gap by exploiting a Majorana canonical basis as the basis of super-operators. In this manner we show that the Liouvillian gap can remain finite in the thermodynamic limit provided the XY model anisotropy parameter remains non-zero. Additionally, we show that the character of the gap with respect to the anisotropy parameter differs depending on the phase of the XY model. The change of character corresponds to the quantum phase transition of the XY model.
14 pages, 10 figures
References in corpus (15)
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- The density-matrix renormalization group in the age of matrix product states
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- The iTEBD algorithm beyond unitary evolution
- Dissipative Phase Transition in Central Spin Systems
- Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- Quantum phase transition in a far from equilibrium steady state of XY spin chain
- Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
- Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
- Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities
- Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
- A matrix product solution for a nonequilibrium steady state of an XX chain
- Rapid mixing and stability of quantum dissipative systems