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arXiv:2004.07797 · Physical review. B./Physical review. B

Non-Gaussian correlations imprinted by local dephasing in fermionic wires

Pavel E. Dolgirev, Jamir Marino, Dries Sels, Eugene Demler

Published Sep 8, 2020• 66 citations
arXivHTMLPDF

Abstract

We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the nonequilibrium steady state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime ruled by strong dissipation, which tames quantum fluctuations. Instances of soluble dissipative impurities represent an experimentally viable platform to understand the interplay between dissipation and Hamiltonian dynamics in many-body quantum systems.

DOI
10.1103/physrevb.102.100301

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We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the nonequilibrium steady state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime ruled by strong dissipation, which tames quantum fluctuations. Instances of soluble dissipative impurities represent an experimentally viable platform to understand the interplay between dissipation and Hamiltonian dynamics in many-body quantum systems.
We consider a quantum wire connected to the leads and subjected to dissipation along its length. The dissipation manifests as tunneling into (out of) the chain from (to) a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem in the nonequilibrium steady state (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. The QPT is identified from the jump of the current and the entropy per site as the dissipation becomes nonzero. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition as a function of the dissipation strength: the particle-particle correlation functions and the response to the electric field exhibit a power-law divergence. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder. Interestingly, we observe a similar transition in the classical dissipative counterflow model: the current has a jump at the ends of the chain introducing an infinitely small dissipation.
We introduce a mapping between the ground state of interacting fermionic Hamiltonians and the non-equilibrium steady state of a purely dissipative open quantum system. Within the framework of third quantization, we map the Fermi-Hubbard Hamiltonian onto Lindblad jump operators acting on Majorana fermions. Remarkably, both hopping and interaction terms map onto jump operators that preserve the Gaussianity of Majorana fermions along individual quantum trajectories. As a result, the dynamics can be unravelled and each trajectory can be simulated efficiently using only two-point correlation functions, with a computational cost that scales polynomially with system size. We further show that finite particle number requires negative dissipative rates, leading to an intrinsically non-Markovian dynamics. The corresponding trajectory unravelling involves both positive and negative stochastic weights and exhibits a sign problem and large fluctuations, so that convergence requires an exponentially large number of trajectories. The overall computational cost remains exponential in system size despite the efficient Gaussian representation of individual trajectories, but is crucially dependent on the computational complexity of the non-Markovian unravelling, motivating further studies on the efficiency of such unravellings.
We analyze the competition between strong correlations and dissipation in quantum impurity systems from the Kondo regime to the valence fluctuation regime by developing a slave-boson theory for a non-Hermitian Anderson impurity model with one-body loss. Notably, in the non-Hermitian Kondo regime, strong correlations qualitatively change the nature of dissipation through renormalization effects, where the effective one-body loss is suppressed and emergent many-body dissipation characterized by the complex-valued hybridization is generated. We unveil the mechanism of a dissipative quantum phase transition of the Kondo state on the basis of this renormalization effect, which counterintuitively enhances the lifetime of the impurity against loss. We also find a crossover from the non-Hermitian Kondo regime to the valence fluctuation regime dominated by one-body dissipation. Our results can be tested in a wide variety of setups such as quantum dots coupled to electronic leads and quantum point contacts in ultracold Fermi gases.
Assuming that the effect of the residual interaction beyond the mean field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of the Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond the mean field is presented first. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states $D=|{\ensuremath{\Phi}}_{a}\ensuremath{\rangle}\ensuremath{\langle}{\ensuremath{\Phi}}_{b}|/\ensuremath{\langle}{\ensuremath{\Phi}}_{b}|{\ensuremath{\Phi}}_{a}\ensuremath{\rangle}$, where $|{\ensuremath{\Phi}}_{a}\ensuremath{\rangle}$ and $|{\ensuremath{\Phi}}_{b}\ensuremath{\rangle}$ are antisymmetrized products of single-particle states. The underlying stochastic mean-field theory is discussed and is applied to the monopole vibration of a spherical 40Ca^{40}\mathrm{Ca}40Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. By restricting to two-particle--two-hole residual interactions, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as $D=|\ensuremath{\Phi}\ensuremath{\rangle}\ensuremath{\langle}\ensuremath{\Phi}|$, where $|\ensuremath{\Phi}\ensuremath{\rangle}$ is a normalized Slater determinant. The associated stochastic Schr\"odinger equation for single-particle wave functions is given.
We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from Jordan-Wigner strings appearing in the jump operators, despite the fact that these models cannot be mapped to quadratic fermionic master equations. We show that many such Lindblad master equations admit an exact stochastic unraveling, with individual trajectories evolving as Gaussian fermionic states, even though the full master equation describes a system inequivalent to free fermions. This allows one to calculate arbitrary observables efficiently without sign problems, and with bounded sampling complexity. We utilize this new technique to study three paradigmatic dissipative effects: the melting of antiferromagnetic order in the presence of local loss, many-body subradiant phenomenon in systems with correlated loss, and nonequilibrium steady states of a 1D dissipative transverse-field Ising model. Beyond simply providing a powerful numerical technique, our method can also be used to gain both qualitative and quantitative insights into the role of interactions in these models.
Quantum many-body systems are characterized by their correlations.While equal-time correlators and unequal-time commutators between operators are standard observables, the direct access to unequal-time anticommutators poses a formidable experimental challenge.Here, we propose a general technique for measuring unequal-time anticommutators using the linear response of a system to a non-Hermitian perturbation.We illustrate the protocol at the example of a Bose-Hubbard model, where the approach to thermal equilibrium in a closed quantum system can be tracked by measuring both sides of the fluctuation-dissipation relation.We relate the scheme to the quantum Zeno effect and weak measurements, and illustrate possible implementations at the example of a cold-atom system.Our proposal provides a way of characterizing dynamical correlations in quantum many-body systems with potential applications in understanding strongly correlated matter as well as for novel quantum technologies.