We study the case of a small quantum spin system S with a non-degenerate groundstate coupled to a small quantum spin bath. Finite temperature measures for both quantum decoherence and thermalization are studied. The computational results, obtained from exact diagonalization, compare well with a recent perturbation theory prediction, even when the system and bath are of comparable sizes.
We study the case of a small quantum spin system S with a non-degenerate groundstate coupled to a small quantum spin bath. Finite temperature measures for both quantum decoherence and thermalization are studied. The computational results, obtained from exact diagonalization, compare well with a recent perturbation theory prediction, even when the system and bath are of comparable sizes.
We study measures of decoherence and thermalization of a quantum system S in the presence of a quantum environment (bath) E. The entirety S+E is prepared in a canonical-thermal state at a finite temperature; that is, the entirety is in a steady state. Both our numerical results and theoretical predictions show that measures of the decoherence and the thermalization of S are generally finite, even in the thermodynamic limit, when the entirety S+E is at finite temperature. Notably, applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider S uncoupled from E, but entangled with E, to predict decoherence and thermalization measures of S. This decoupling allows closed-form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of S and of E. Large-scale numerical results for both coupled and uncoupled entireties with up to 40 quantum spins support these findings.
In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.
It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state, and system-bath coupling strength, using the steady-state value of magnetization as a probe. Focusing on nonequilibrium dynamics and steady-state properties, our results indicate that within system sizes amenable to exact diagonalization, a strongly localized system interacting in a junction configuration retains remnant information on its initial state at long times despite coupling to a finite ergodic environment. In contrast, in a ladder configuration, strong dependencies on the initial state and coupling strength are observed, which can lead to either the loss or retention of information. Finally, we highlight and discuss discrepancies that can arise when similar methodologies are employed to infer localization or thermalization, revealing the need for careful interpretation.
We present an exactly solvable model to study the role of the system-bath coupling for the generalized canonical thermalization, which reduces almost all the pure states of the ``universe'' (formed by a system S plus its surrounding heat bath B) to a canonical equilibrium state of S. It is found that, for the overwhelming majority of the ``universe'' states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, a decoherence mechanism is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. The nonvanishing off-diagonal elements due to the finite size of the bath and the stronger system-bath interaction might offer more to quantum thermalization.
We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest-neighbor interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.
We study the decoherence of a qubit weakly coupled to frustrated spin baths. We focus on spin baths described by the classical Ising spin glass and the quantum random transverse Ising model which are known to have complex thermodynamic phase diagrams as a function of an external magnetic field and temperature. Using a combination of numerical and analytical methods, we show that for baths initially in thermal equilibrium, the resulting decoherence is highly sensitive to the nature of the coupling to the environment and is qualitatively different in different parts of the phase diagram. We find an unexpected strong non-Markovian decay of the coherence when the random transverse Ising model bath is prepared in an initial state characterized by a finite temperature paramagnet. This is contrary to the usual case of exponential decay (Markovian) expected for spin baths in finite temperature paramagnetic phases, thereby illustrating the importance of the underlying nontrivial dynamics of interacting quantum spinbaths.