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Kramers degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility property of systems at thermal equilibrium - the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the standard Greens functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results suggest that time-reversal symmetry of the system-bath Hamiltonian can affect open system dynamics only if the bath is in thermal equilibrium.
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Kramers theorem ensures double degeneracy in the energy spectrum of a time-reversal symmetric fermionic system with half-integer total spin. Here we are now trying to go beyond the closed system and discuss Kramers degeneracy in open systems out of equilibrium. In this letter, we prove that the Kramers degeneracy in interacting fermionic systems is equivalent to the degeneracy in the spectra of different spins together with the vanishing of the inter-spin spectrum. We find the violation of Kramers degeneracy in time-reversal symmetric open quantum systems is locked with whether the system reaches thermal equilibrium. After a sudden coupling to an environment in a time-reversal symmetry preserving way, the Kramers doublet experiences an energy splitting at a short time and then a recovery process. We verified the violation and revival of Kramers degeneracy in a concrete model of interacting fermions and we find Kramers degeneracy is restored after the local thermalization time. By contrast, for time-reversal symmetry $tilde{cal T}$ with $tilde{cal T}^2=1$, we find although there is a violation and revival of spectral degeneracy for different spins, the inter-spin spectral function is always nonzero. We also prove that the degeneracy in spectral function protected by unitary symmetry can be maintained always.
We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries. By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of multiple, commuting, invariant subspaces we derive a tight lower bound for the stationary state degeneracy. We apply these results within the context of open quantum many-body systems, presenting three illustrative examples: a fully-connected quantum network, the XXX Heisenberg model and the Hubbard model. We find that the derived bound, which scales at least cubically in the system size the $SU(2)$ symmetric cases, is often saturated. Moreover, our work provides a theory for the systematic block-decomposition of a Liouvillian with non-Abelian symmetries, reducing the computational difficulty involved in diagonalising these objects and exposing a natural, physical structure to the steady states - which we observe in our examples.
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.
We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions within the differential equation for the populations that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Greens functions and self-energies plays a pivotal role in determining these decay rates.
We study heating dynamics in isolated quantum many-body systems driven periodically at high frequency and large amplitude. Combining the high-frequency expansion for the Floquet Hamiltonian with Fermis golden rule (FGR), we develop a master equation termed the Floquet FGR. Unlike the conventional one, the Floquet FGR correctly describes heating dynamics, including the prethermalization regime, even for strong drives, under which the Floquet Hamiltonian is significantly dressed, and nontrivial Floquet engineering is present. The Floquet FGR depends on system size only weakly, enabling us to analyze the thermodynamic limit with small-system calculations. Our results also indicate that, during heating, the system approximately stays in the thermal state for the Floquet Hamiltonian with a gradually rising temperature.
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