We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamiołkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.
Symmetry transformations have proved useful in determining the algebraic structure and internal dynamical properties of physical systems. In the quantum Rabi model, invariance under parity symmetry transformation has been used to obtain exact solutions of the eigenvalue equation and very good approximations of the internal dynamics of the interacting atom-light system. In this article, two symmetry operators, characterized as "duality" symmetry operators, have been introduced which transform the quantum Rabi Hamiltonian into duality conjugates. The parity and duality symmetry operators constit…
We present a theoretical analysis of the dynamics of a one-dimensional spin-1/2 fermionic gas subject to weak two-body losses. Our approach highlights the crucial role played by spin conservation in the determination of the full time evolution. We focus in particular on the dynamics of a gas that is initially prepared in a Dicke state with fully-symmetric spin wavefunction, in a band insulator, or in a Mott insulator. In the latter case, we investigate the emergence of a steady symmetry-resolved purification of the gas. Our results could help the modelisation and understanding of recent experi…
We analyze a general method for the dissipative preparation and stabilization of volume-law entangled states of fermionic and qubit lattice systems in 1D (and higher dimensions for fermions). Our approach requires minimal resources: nearest-neighbour Hamiltonian interactions that obey a suitable chiral symmetry, and the realization of just a single, spatially-localized dissipative pairing interaction. In the case of a qubit array, the dissipative model we study is not integrable and maps to an interacting fermionic problem. Nonetheless, we analytically show the existence of a unique pure entan…
We predict a new mechanism to induce collective excitations and a nonequilibrium phase transition of fermionic superfluids via a sudden switch-on of two-body loss, for which we extend the BCS theory to fully incorporate a change in particle number. We find that a sudden switch-on of dissipation induces an amplitude oscillation of the superfluid order parameter accompanied by a chirped phase rotation as a consequence of particle loss. We demonstrate that when dissipation is introduced to one of the two superfluids coupled via a Josephson junction, it gives rise to a nonequilibrium dynamical pha…
Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）
We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. We focus on the hydrodynamic limit of large distances from the source of dissipation and of long times, with their ratio being fixed. In this limit, the localized dissipation gives rise to an effective delta potential (dissipative impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic descriptio…
We revisit statistical wavefunction properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength $λ$, the strength functions $F_k(E)$ are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio $ξ_2$ and the information entropy $S…
We formulate and discuss explicit computation of dynamic correlation functions in open quadradic fermionic systems which are driven and dissipated by the Lindblad jump processes that are linear in canonical fermionic operators. Dynamic correlators are interpreted in terms of local quantum quench where the pre-quench state is the non-equilibrium steady state, i.e. a fixed point of the Liouvillian. As an example we study the XY spin 1/2 chain and the Kitaev Majorana chains with boundary Lindblad driving, whose dynamics exhibits asymmetric (skewed) light cone behaviour. We also numerically treat …
By extending local U(1) gauge symmetry to discontinuous case, we find that under one special discontinuous U(1) gauge transformation the symmetric and antisymmetric wave functions can transform into each other in one dimensional quantum mechanics. The free spinless fermionic system and bosonic system with $δ$-type vector gauge potential are proved to be equivalent. The relation also holds in higher space-time dimensions.
Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition …
A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely the bound state and the modified Laplace transformation are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environm…
For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $δ$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $ε$-interaction, solvable many-body problem, exact bosonization
Quantized vortices carry the angular momentum in rotating superfluids, and are key to the phenomenon of quantum turbulence. Advances in ultra-cold atom technology enable quantum turbulence to be studied in regimes with both experimental and theoretical control, unlike the original contexts of superfluid helium experiments. While much work has been performed with bosonic systems, detailed studies of fermionic quantum turbulence are nascent, despite wide applicability to other contexts such as rotating neutron stars. In this paper, we present the first large-scale study of quantum turbulence in …
