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Register a new userViolation and Revival of Kramers Degeneracy in Open Quantum Systems
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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.
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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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At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid $^4$He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid the entropy and density oscillations are strongly coupled, and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.
We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.
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