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Register a new userMany-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics
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We study the impact of the inter-level energy constraints imposed by Haldane Exclusion Statistics on relaxation processes in 1-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock space, we identify certain universal features of this relaxation dynamics, and show that it is generically slower than that of spinless fermions. Our study focuses on the Calogero-Sutherland model, which realizes Haldane Exclusion statistics exactly in one dimension; however our results apply to any system that has the associated pattern of inter-level occupancy constraints in Fock space.
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We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension that is relevant to experiments on Rydberg atoms in the antiblockade regime. These states provide a new solvable example of quantum many-body scars: their sub-volume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals, which persist as approximate revivals on a finite timescale when the underlying model is perturbed. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices.
We study the frequency dependence of the optical conductivity $text{Re} , sigma(omega)$ of the Heisenberg spin-$1/2$ chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random $z$-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform $text{Re} , sigma(omega)$ for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of $text{Re} , sigma(omega)$ is well described by $text{Re} , sigma(omega) approx sigma_text{dc} + a , |omega|^alpha$, with $alpha approx 1$ in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of $sigma_text{dc}$ in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of $sigma_text{dc}$ is consistent with the existence of a mobility edge.
The low energy properties of the one-dimensional anyon gas with $delta$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter $alpha$ is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of $alpha$ in the dispersion relations.
We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some landmarks within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).
A powerful perspective in understanding non-equilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, not much else is known about the refined characters of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagation out-of-equilibrium, from the view of entanglement Hamiltonian. As a prototypical example, we study quantum quench dynamics of a one-dimensional Bose-Hubbard model by means of time-dependent density-matrix renormalization group simulation. Before reaching equilibration, it is found that a current operator emerges in entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, entanglement temperature of steady state is spatially independent, which provides an intuitive trait of equilibrium. We demonstrate that these features are consistent with predictions from conformal field theory. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from perspective of entanglement Hamiltonian.
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