Exact description of fermionic reservoirs via purified damped ancillary fermions

We present a method for the modeling of fermionic reservoirs using a new class of ancillary damped fermions, dubbed purified pseudofermions, which exhibit unusual free correlations. We show that this key feature, when combined with existing efficient decomposition algorithms for the reservoir correlation functions, enables the development of an easily implementable and accurate scheme for constructing effective models of fermionic reservoirs. We numerically demonstrate the validity, accuracy, efficiency and potential use of our method by studying the particle transport of spinless fermions in a one-dimensional chain. Beyond its utility as a quantum impurity solver, our method holds promise for addressing a wide range of problems involving extended systems in fields like quantum transport, quantum thermodynamics, thermal engines and nonequilibrium phase transitions.

💡 Research Summary

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The paper introduces a novel framework for modeling fermionic reservoirs in open quantum systems by extending the pseudo‑fermion approach with a new class of “purified damped ancillary fermions.” Conventional pseudo‑fermion methods approximate the continuous hybridization function (J(\varepsilon)) and the Fermi distribution (f(\varepsilon)) of a reservoir with a set of discrete, damped auxiliary fermions. Each auxiliary mode is characterized by four parameters (energy (\varepsilon), decay rate (\gamma), coupling amplitude (\lambda), and average occupation (n)). While this representation is exact in principle, realistic reservoirs often possess sharp band edges, low‑temperature Fermi steps, or other intricate spectral features that demand a large number of auxiliary modes. Consequently, the parameter space becomes high‑dimensional ((8N_{\text{pf}}) real variables) and standard nonlinear optimization becomes computationally prohibitive.

The authors solve this bottleneck by defining “purified pseudo‑fermions.” Starting from a conventional pseudo‑fermion, they analytically continue its frequency and decay rate into the complex plane along the paths (\varepsilon\to\varepsilon\pm i a) and (\gamma\to\gamma+a) with (a\to+\infty). Simultaneously the occupation number is fixed to either 0 or 1. This limiting procedure yields four distinct types (I, II, III, IV) whose free two‑time correlation matrices are extremely sparse: each matrix contains a single non‑zero entry, either the particle‑particle component for positive times or the hole‑hole component for negative times. Explicitly, \