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arXiv:1606.09122 · Physical Review Letters

Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise

Mariya V. Medvedyeva, Fabian H. L. Eßler, Tomaž Prosen

Published Sep 21, 2016• 162 citations
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Abstract

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

DOI
10.1103/physrevlett.117.137202

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We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.
Abstract We theoretically investigate the many-body dynamics of a tight-binding chain with dephasing noise on an infinite interval. We obtain the exact solution of the average particle-density profile for the domain wall and the alternating initial conditions via the Bethe ansatz, analytically deriving the asymptotic expressions for the long-time dynamics. For the domain wall initial condition, we obtain the scaling form of the average density, elucidating that diffusive transport always emerges in the long-time dynamics if the strength of the dephasing, no matter how small, is positive. For the alternating initial condition, our exact solution leads to the fact that the average density displays oscillatory decay or overdamped decay depending on the strength of the dissipation. Furthermore, we demonstrate that the asymptotic forms approach those of the symmetric simple exclusion process, identifying corrections from it.
We present a Bethe-ansatz-solvable dissipative model of one-dimensional hard-core anyons under dephasing, where the particles obey fractional statistics. We establish an exact mapping between the Liouvillian and a non-Hermitian Hubbard model with special twisted boundary conditions. With the help of string hypothesis, we rigorously calculate the finite-size corrections and the Liouvillian gap in terms of the statistical parameter, total particle number, lattice size, and dissipation strength. The statistical parameter breaks the $\ensuremath{\eta}$-pairing symmetry of the system, partially lifts out the degeneracy of the spectrum, and contributes to the Liouvillian gap in finite-size corrections. We also derive the general form of the equation of motion for expectation values of the 2w2w2w-point correlator of hard-core anyons and present a proposal for experimentally measuring the correlation function. Our results shed light on the Liouvillians of exactly solvable dissipative models of anyonic particles that obey the fractional statistics.
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
The full counting statistics (FCS) of current has long provided fundamental insights into nonequilibrium systems. Recently, the FCS in quantum many-body systems has attracted growing attention, driven by rapid experimental progress in measuring current fluctuations. Nevertheless, for diffusive quantum many-body dynamics, the FCS of current has yet to be obtained exactly. In this Letter, we present the first exact solution for the FCS of current in a diffusive quantum many-body system, specifically a tight-binding chain with dephasing noise. By leveraging the system's SU(2) symmetry and a mapping to the one-dimensional Hubbard model, we derive an exact Fredholm determinant representation for the moment generating function of the time-integrated current. Our long-time asymptotic analysis shows that the cumulant generating function, and hence the corresponding large-deviation function, exhibit diffusive scaling for any nonzero dephasing. We compare our theoretical predictions with experimentally measured current variance and find consistent diffusive scaling.
We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.
Abstract We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.